Democrats made strong showings through most of the East yesterday, but in New York's gubernatorial contest that was considered a referendum on Reaganomics, liberal Democrat Mario M. Cuomo managed only a razor-thin victory over conservative supply-side Republican Lewis E. Lehrman.

While Cuomo was claiming his victory late last night, Lehrman was demanding a recount.

In neighboring New Jersey, first-time Democratic candidate Frank R. Lautenberg upset favored Republican Rep. Millicent Fenwick in their tightly contested race for the Senate. But Republicans had a surprise of their own in the region, as New Hampshire Republican John Sununu upset incumbent Democratic Gov. Hugh Gallen.

In the East's Senate races, the incumbents won reelection -- but three of the region's moderate Republican senators managed to hang on only by the narrowest of margins. Sens. Robert T. Stafford (R-Vt.) and Lowell P. Weicker Jr. (R-Conn.) were reelected by thin margins. And Sen. John H. Chafee (R-R.I.) was the apparent winner in a contest against former state attorney general Julius C. Michaelson that was even closer. In Pennsylvania, another moderate Republican, Sen. John Heinz, won a one-sided victory.

Democratic Senate incumbents won convincingly. Senate fixtures Robert C. Byrd of West Virginia, the minority leader, and Edward M. Kennedy of Massachusetts swept to easy victories, as did first term incumbents Daniel Patrick Moynihan of New York and Paul S. Sarbanes of Maryland.

In Maine, appointed Democratic Sen. George Mitchell was also reelected, in a contest he had been expected to lose earlier in the year.

In the gubernatorial races, moderate Republican Richard L. Thornburgh of Pennsylvania was reelected over Rep. Allen E. Ertel, in a race that was closer than expected, and Vermont Republican Gov. Richard A. Snelling was reelected.

Incumbent Democratic governors Harry R. Hughes of Maryland won reelection handily, as did Connecticut's William A. O'Neill. And former governor Michael S. Dukakis of Masschusetts was returned to the governship he held four years ago, a victory that was expected once he defeated his former nemesis, conservative Democrat Edward J. King, in this year's primary. Gov. Joseph E. Brennan (D) of Maine also was reelected.

According to ABC exit polling, women voters were an important factor in New Jersey and New York. In New Jersey, women tended to vote for the male Democratic Party candidate and not the woman candidate on the Republican line, Fenwick.

In New York, Cuomo was winning the votes of women by a significant plurality, but he was losing among male voters.

In one of the nation's most publicized congressional races, Rep. Barney Frank (D-Mass.) defeated Rep. Margaret Heckler (R-Mass.) in a battle of incumbents caused by redistricting. CONNECTICUT

Incumbent Sen. Lowell P. Weicker Jr. (R) narrowly defeated his challenger, Rep. Toby Moffett (D), in a closely fought contest between two liberal mavericks in Congress.

Both camps had counted on final organization get-out-the-vote efforts to provide the margin of victory.

A Conservative Party candidate, Lucien DiFazio, 39, was believed to have siphoned some of the normally conservative Republican votes from Weicker.

Gov. William A. O'Neill (D) easily defeated his gubernatorial opponent, state Sen. Lewis B. Rome (R).

In the district vacated by Moffett, state Sen. Nancy L. Johnson (R) was running slightly ahead of William E. Curry Jr. (D). With almost seven-eighths of the vote counted, she had received about 52 percent of the vote.

Freshman Rep. Sam Gejdenson (D) had a substantial lead over insurance man Tony Guglielmo (R), whom he defeated two years ago. DELAWARE

William V. Roth Jr., the Republican senator whose name was tacked on top of the Reagan tax reform bill, swept easily to a third term over David N. Levinson, 46, a Middletown real estate developer despite Levinson's nice slogan describing the administration's program as the "grapes of Roth."

The contest for Delaware's only seat in the House went to the challenger, Democratic state treasurer Thomas R. Carper, 35, of New Castle. Carper took 53 percent of the vote over three-term U.S. Rep. Thomas B. Evans Jr. (R), 50, of Wilmington.

Evans had suffered from a link with lobbyist and Playboy model Paula Parkinson. Carper survived a late-campaign article in the New York Post reporting allegations of wife and child abuse stemming from a child-custody dispute that was settled out of court. Carper said "the implications in that article are without basis in fact." MAINE

In the key Maine campaign, incumbent Sen. George J. Mitchell (D), 49, defeated Rep. David F. Emery (R), 34.

The White House believed this was one of the few Senate contests where a Democratic incumbent might be defeated.

Mitchell, appointed in 1980 to fill Sen. Edmund S. Muskie's unexpired term, had never been elected to public office, and Republicans hoped to win the seat for the first time in 30 years.

But Emery, plagued throughout the summer by campaign blunders, lost his early lead.

Meanwhile, in a close race for Emery's vacated House seat between state Sen. John M. Kerry (D) and former state representative John R. (Jock) McKernan (R), were running neck-and-neck.

Gov. Joseph E. Brennan (D), 47, easily defeated Charles L. Cragin (R), 39, to win a second term and Olympia J. Snowe (R), 35, won a third House term. MASSACHUSETTS

Former governor Dukakis (D), 48, easily defeated John W. Sears (R), 51, keeping the statehouse in Democratic hands.

In the state's Senate race, Kennedy (D), 50, won by a wide margin over businessman Raymond Shamie (R), 61, extending his 20-year career in the Senate.

The only question in that race was the size of Kennedy's victory. Republicans wanted to keep Kennedy under 60 percent of the vote to damage his chances if he decides to run for president in 1984, but early returns had Kennedy running over that figure.

In the most exciting Massachusetts race, pitting two House incumbents against one another, Margaret Heckler (R), 51, conceded defeat to liberal Barney Frank (D), 42. Frank was leading by a margin of about 2 to 1. The two were thrown into competition by redictricting. Heckler, seeking her ninth term in Congress, is the senior woman in Congress.

Frank, who raised $1 million for his race, campaigned on the issue of Heckler's support for the Reagan economic program, which is unpopular in Massachusetts.

The other incumbents in the House delegation -- nine Democrats and one Republican -- were all expected to win reelection. MARYLAND

Maryland voters decided to stand pat, reelecting their governor, their senator and all their congressmen.

Sen. Paul S. Sarbanes (D), 49, jarred into campaign activity early by an attack from the National Conservative Political Action Committee (NCPAC), was getting almost 60 percent of the vote over Prince George's County Executive Lawrence J. Hogan (R), 53.

Gov. Harry R. Hughes (D) was getting slightly better than 60 percent of the vote as he won a second term by defeating Anne Arundel County Executive Robert A. Pascal, 47 (R).

All eight incumbent House members in the state were reelected, including the three from the Washington suburbs -- Marjorie S. Holt, the only Republican in the state delegation, and Steny H. Hoyer and Michael D. Barnes. NEW HAMPSHIRE

Incumbent Gov. Hugh Gallen (D), 58, lost his battle against challenger John Sununu (R), 43, a conservative from southern New Hampshire.

With no Senate race and both incumbent congressmen expected to win, the key campaign in New Hampshire this year was the gubernatorial fight.

Gallen, who defeated ultra-conservative Meldrim Thomson in 1978 and again in 1980, was seeking a third term but ran into problems by refusing to pledge to veto a state sales or income tax. Sununu, an engineering professor at Tufts University near Boston, promised the tax veto.

New Hampshire is the only state in the country that has neither tax. The veto "pledge" has been made by every successful gubernatorial candidate in the last decade. Gallen took it in both 1978 and 1980.

Meanwhile, Thomson filed in the governor's race as an independent in case a moderate won the GOP primary.

He endorsed Sununu but remained on the ballot and received a small percentage of the vote. NEW JERSEY

Montclair computer executive Frank Lautenberg (D) spent a substantial amount of his own money in a successful attempt to defeat Rep. Millicent Fenwick (R) in the contest to see who would take Abscam-tainted Harrison (Pete) Williams' Senate seat.

Staff writers Martin Schram, Mary Thornton and Douglas B. Feaver contributed to this report.

Fenwick, the four-term congresswoman who is generally regarded as the model for the Doonesbury comic strip character Lacey Davenport, had a huge early lead in the polls, but Lautenberg campaigned and spent vigorously and polls showed he had caught her by last weekend; with most of the vote counted last night he was holding 52 percent.

All New Jersey House incumbents save one were reelected. That one, three-term Republican Harold C. Hollenbeck, 43, was knocked off by Democratic whiz kid Robert G. Torricelli, 31, a former aide to Vice President Mondale. Torricelli polled 54 percent of the vote.

Five-term incumbent Rep. Matthew J. Rinaldo (R) was getting 56 percent of the vote despite a million-dollar campaign by Adam K. Levin (D), former state consumer affairs director. NEW YORK

In the New York gubernatorial race, Lt. Gov. Cuomo, 50, had portrayed multimillionaire businessman Lehrman as one of the early architects of President Reagan's economic policy of cutting taxes and domestic spending.

Lehrman, 44, contributed to the supply-side ideas that shaped Reagan's initial economic policies and had also proposed in this campaign his own plan of steep tax cuts for the state.

Sen. Daniel Patrick Moynihan, the Democratic and Liberal Party nominee, scored an expected landslide victory over Assemblywoman Florence Sullivan, 51, the candidate of the Republican, Conservative and Right to Life parties.

In two congressional races, incumbents were forced by redistricting to run against each other. Rep. Guy V. Molinari (R) was projected by ABC as the winner over Rep. Leo C. Zeferetti (D) in a new district that contained large chunks of Molinari's former Staten Island base. Rep. Benjamin A. Gilman (R) was leading in his race with Rep. Peter A. Peyser (D).

Rep. John LeBoutillier (R), a staunch conservative freshman, faced a tough race against Suffolk County legislator Robert J. Mrazek (D), who was projected a winner by local GOP officials after early returns. PENNSYLVANIA

Incumbent Gov. Richard L. Thornburgh (R), predicted to be a runaway winner over Rep. Allen E. Ertel (D), was locked in a tight race all evening before finally pulling away to victory.

Sen. John Heinz (R), defending for the first time, was able to raise a substantial war chest without dipping into his own funds and easily won reelection over Allegheny County (Pittsburgh) Commissioner Cyril H. Wecht.

According to the AP, 18 incumbents were reelected to the House. In the other races:

Wilkes-Barre lawyer Frank Harrison (D) defeated incumbent James L. Nelligan (R) with 54 percent of the vote.

State Rep. Joseph P. Kolter (D) was projected by ABC to have defeated incumbent Eugene V. Atkinson (R). Atkinson, elected as a Democrat in 1980, changed parties and was targeted with a heavy Democratic effort.

Former congressman Peter H. Kostmayer (D) was projected by ABC as a winner over incumbent Jim Coyne (R) in a grudge rematch.

In the 18th, incumbent Doug Walgren (D) was getting 56 percent of the vote in a challenge from Ted Jacob (R).

In the 21st, where Marc L. Marks retired, the AP said Anthony Andrezski (D) had managed a narrow victory over and Thomas J. Ridge (R), but both candidates were claiming victory and a recount seemed possible. RHODE ISLAND

Incumbent Sen. John H. Chafee (R), 59, apparently won a razor-thin victory over his challenger, former state attorney general Julius C. Michaelson (D), 60. With 99 percent of the vote counted, Chafee had a lead of about 1.5 percent, so narrow that it could theoretically be overturned when absentee ballots are counted.

Chafee, who spent over $1 million seeking a second Senate term, was in the awkward position of being a moderate Republican under attack for the Reagan administration's economic policies in an overwhelmingly Democratic state.

Meanwhile, Gov. J. Joseph Garrahy (D), 51, easily won a fourth term, defeating Vincent Marzullo (R), 35, a solar energy consultant. Marzullo, a former Democrat who registered as a Republican in June when he announced his candidacy, was not a serious threat.

Both of Rhode Island's House members, Claudine Schneider (R) and Fernand J. St Germain (D), were leading and expected to win easily. VERMONT

Incumbent Sen. Robert T. Stafford (R), 69, held an extremely narrow lead over his challenger, former Vermont secretary of state James A. Guest (D), 41, and was projected by CBS and ABC as the winner.

Stafford went into the election holding onto a shaky lead, but with the Republican Party clearly worried about the possibility of losing the seat.

In the gubernatorial campaign, Gov. Richard A. Snelling (R), 55, defeated challenger Lt. Gov. Madeleine M. Kunin (D), 49, and won an unprecedented fourth term.

Snelling's campaign benefited from Vermont's relatively low unemployment rate--just over half the nationwide figure. Meanwhile, James M. Jeffords (R), the state's only House member, easily defeated his five challengers. WEST VIRGINIA

Senate Minority Leader Robert C. Byrd was elected for the fifth time and Democrats appeared to be in a position to take all four House seats. Byrd had little trouble with Rep. Cleve Benedict (R), who abandoned his House seat to make the race.

In that district, Harley O. Staggers Jr. (D), son of the man who held the seat for 32 years, recaptured it for the family, according to both AP and ABC, and was getting almost two-thirds of the vote.

Alan B. Mollohan (D), according to AP, won in the 1st District by defeating state Rep. John F. McCuskey (R). That district is presently held by Mollohan's father, Robert H. Mollohan.

Bob Wise (D), Charleston state senator, was getting 61 percent of the early vote in an attempt to unseat first-term incumbent David Michael Staton (R). Incumbent Nick J. Rahall (D), was declared the winner by AP over retired railroad worker Homer L. Harris (R).