Consumer lawyer Mark Green, outspent 10 to 1, scored a stunning upset last night over millionaire businessman John S. Dyson in the New York Democratic Senate primary battle to challenge Republican Sen. Alfonse M. D'Amato.

Green's victory came on the busiest day of the primary season, when nine states picked gubernatorial and House candidates and seven held Senate primaries.

With 95 percent of the precincts reporting in a race marked by very low turnout, Green had 53 percent of the vote to Dyson's 47 percent. Dyson spent about $ 6 million, most of it his own money, to about $ 600,000 for Green.

Green, a former colleague of consumer activist Ralph Nader, displayed a talent for getting free news media coverage, however, and had a strong liberal base in New York City, which cast more than half the state's Democratic primary vote yesterday.

At his victory celebration last night, Green said, "There's still some doubters and pundits who will say, 'You can't win, Green. D'Amato has too much money.' Where have we heard that before?"

In the Wisconsin Democratic senatorial primary, Deputy Attorney General Edward R. Garvey, former executive director of the National Football League Players' Association, defeated former state Democratic chairman Matthew J. Flynn.

In Minnesota, St. Paul Mayor George Latimer conceded defeat to Gov. Rudy Perpich in the Democratic-Farmer-Labor Party primary. Perpich was the only incumbent governor to face serious opposition yesterday.

In Connecticut, state Rep. Julie D. Belaga won the Republican gubernatorial nomination and will face Democratic Gov. William A. O'Neill on Nov. 4. Belaga received a plurality of 41 percent to defeat two former state senators. Roger Eddy was unopposed for the Republican Senate nomination. In New Hampshire, Endicott Peabody, former governor of Massachusetts, won the Democratic Senate nomination. Peabody was carrying more than 60 percent against three other candidates and will face Republican Sen. Warren B. Rudman.

In Rhode Island, Bruce G. Sundlun, a millionaire political newcomer, easily won the Democratic gubernatorial nomination with about 75 percent of the vote in his contest against a former radio talk show host.

None of the five senators running for reelection -- three Republicans, two Democrats -- had strong opposition for nomination. There were two open Senate seats. D'Amato, Rudman and Sen. Robert W. Kasten Jr. (R-Wis.) faced no significant opposition in the Republican primaries. Democratic Sens. Patrick J. Leahy (Vt.) and Christopher J. Dodd (Conn.) also were unopposed.

Democratic Govs. Mario M. Cuomo of New York, Connecticut's O'Neill, Anthony S. Earl of Wisconsin and Madeleine M. Kunin of Vermont faced little or no opposition, as did Republican Govs. Edward DiPrete of Rhode Island and John H. Sununu of New Hampshire.

Arizona and Maryland, however, had strenuous races for open gubernatorial seats. In Arizona, four millionaires -- two Democrats and two Republicans -- battled for their parties' nominations.

In Arizona, Rep. John S. McCain III was unopposed in the GOP primary and former state corporation commissioner Richard Kimball faced token opposition in the Democratic primary. McCain, a former Vietnam prisoner of war, enters the fall campaign as a favorite.

In Minnesota, Republican former governor Harold Stassen, who has been trying to make a political comeback for nearly 40 years, was nominated for Congress in his home district in St. Paul. Stassen will face Rep. Bruce Vento (D).

On a day dubbed "Super Tuesday for Women" by one feminist group, female candidates were scoring breakthroughs in several states.

Belaga, a former teacher, became the first woman to win the GOP gubernatorial nomination in Connecticut, upsetting two male opponents. Vermont Gov. Kunin (D) was renominated for a second term without opposition, while Maryland nominated two women to face each other in an open race for the U.S. Senate.

Former representative Bella Abzug (D-N.Y.), facing three opponents, was in a tight contest in her attempt at a political comeback in a suburban New York congressional district. With about 90 percent of the vote counted, Abzug led Oren Teicher, 36 to 34 percent.

There were 23 women who sought nomination to statewide office yesterday; 14 more sought congressional nominations.

Here is a state-by-state breakdown of yesterday's races:

Arizona

This is a pivotal year in Arizona politics. Two popular officeholders, Republican Sen. Barry Goldwater and Democratic Gov. Bruce E. Babbitt, are not seeking reelection. Two of the state's five House seats are open, and the longtime occupant of a third, House Interior Committee Chairman Morris K. Udall (D), faced a rare primary election challenge.

In the hotly contested Democratic gubernatorial primary, state school Supt. Carolyn Warner took an early lead over Tony Mason, a Phoenix lawyer and developer. David Moss, who had dropped out of the race and endorsed Mason, remained on the ballot.

In the race for the Republican gubernatorial nomination, auto dealer Evan Mecham was running in front of Arizona House Majority Leader Burton Barr, the favorite in the race.

Udall, first elected in 1961, was having little difficulty turning back a challenge by state Sen. Luis Gonzales of Tucson, although Udall's district is 35 percent Hispanic.

Jay Rhodes, son of former House Republican leader John J. Rhodes, was favored to win a four-way race for nomination to the 1st Congressional District seat being vacated by Rep. John S. McCain III (R). Polls showed his chief opposition coming from Ray Russell, a Mesa veterinarian, and Rick C. Lavis, executive vice president of the Arizona Cotton Growers Association. Harry Braun was unopposed in the Democratic primary.

In another spirited GOP congressional primary, former congressman John B. Conlan attempted a comeback against Jon Kyl and Mark Dioguardi, both Phoenix lawyers, in the 4th district.

Connecticut

State House Deputy Majority Leader Julie D. Belaga won easily over two other Republicans in the battle to take on Democrat Gov. William A. O'Neill, who was unopposed in the primary and favored to win reelection. She edged state Sen. Richard C. Bozzuto, a Watertown insurance agent who was endorsed by the state GOP convention in July. Former state senator Gerald Labriola was a distant third.

Belaga, the first woman to seek the GOP gubernatorial nomination in Connecticut, is a former teacher who has served in the General Assembly for a decade. She was one of three women to seek nomination to statewide office in Connecticut yesterday.

O'Neill, who has been in office six years, avoided a primary challenge when former U.S. representative Toby Moffett (D-Conn.) narrowly failed to muster the 20 percent support he needed at the state Democratic convention to get on the ballot.

Minnesota

Gov. Rudy Perpich rode out a primary challenge from St. Paul Mayor George Latimer for the Democratic-Farmer-Labor (DFL) Party nomination for another term.

Latimer, one of the most liberal politicians in the state, appealed for Republicans, disillusioned with their own party choices in the primary, and independents to cross over and vote for him in the DFL primary. Latimer was endorsed by prominent Twin Cities area businessmen, including the 1982 Independent-Republican (IR) Party nominee, Wheelock Whitney, but polls indicated that his hopes of upsetting Perpich with a big primary vote in Minneapolis and St. Paul had failed.

Latimer, who challenged Perpich because of "his lack of vision," picked Arvonne Fraser, wife of Minneapolis Mayor Don Fraser, to run as his lieutenant governor candidate, a move that angered many rural DFL adherents. Perpich, who has said his reelection would be a "cakewalk" if it weren't for Latimer, also had a female running mate, Lt. Gov. Marlene Johnson.

Former state representative Cal Ludeman, a Tracy farmer endorsed by the IR state convention, defeated Bloomington Mayor James Lindau for his party's gubernatorial nomination. But a perceived takeover of the IR by fundamentalist Christians has badly divided the party, and Ludeman is expected to face an uphill battle Nov. 4.

New Hampshire

Sen. Warren B. Rudman had no Republican senatorial primary opposition because a state Ballot Law Commission ruling forced former Pentagon Strategic Defense Initiative (SDI) spokesman Bruce Valley to run as an independent rather than as a Republican as he had hoped. On the Democratic side, Endicott Peabody easily gained the senatorial nomination by defeating three opponents: former Nashua alderman Robert Dupay, the Rev. Andrew Tempelman and Robert Patton, a follower of extremist Lyndon H. LaRouche Jr.

Seabrook, the state's controversial nuclear power plant, was an issue for Republicans and Democrats in the gubernatorial primaries. Gov. John H. Sununu (R) defeated state Rep. Roger Easton, who criticized him for supporting construction of the Seabrook plant. In the Democratic gubernatorial primary, Paul McEachern, a Portsmouth lawyer, defeated two other candidates, Paul Gagnon, a county prosecutor from Manchester, and solar energy expert Bruce Anderson. All three had opposed the plant.

Rep. Robert C. Smith (R) defeated Louis J. Georgopoulos, a local officeholder in Manchester.

New York

Democratic senatorial primary candidate Mark Green was endorsed by Reps. Ted Weiss, Stephen J. Solarz and Major R. Owens, all Democratic congressmen from New York City, and 31 state legislators, including blacks, Hispanics, Jews and white liberals, also mostly from New York City.

His opponent, John Dyson, however, was supported by the Democratic Party leadership, and while Gov. Mario M. Cuomo professed neutrality, he said Dyson was the candidate with enough money to challenge Sen. Alfonse M. D'Amato (R-N.Y.), who has raised more than $ 5 million. With the help of some of Cuomo's supporters, Dyson also won the Liberal Party endorsement and will be on the Nov. 4 ballot regardless of the primary results.

Former representative Bella Abzug (D), who served three terms in the House from Manhattan before making an unsuccessful Senate race in 1976, was holding a slim lead in her four-way House nomination battle. She is trying for a political comeback in the suburban Westchester County House district represented by first-term Rep. Joseph J. DioGuardi (R). Abzug's closest competitor was the man who won the Democratic nomination in 1984, Oren Teicher. With 97 percent of the vote counted, Abzug had 36 percent, while Teicher had 34 percent.

In the four-way Democratic primary in the Queens district long represented by Rep. Joseph P. Addabbo (D), who died last April, Rep. Alton R. Waldon Jr. (D) was defeated after holding the post for only a few months after his June special election. The Rev. Floyd Flake, the winner, gathered 48 percent of the vote to Waldon's 41 percent, with two other candidates far behind.

Rhode Island

Bruce G. Sundlun, a millionaire political newcomer, won the Democratic gubernatorial nomination and will oppose Gov. Edward D. DiPrete, a first-term Republican who won a landslide election in the usually Democratic state two years ago.

Vermont

Only former governor Richard Snelling (R), who is challenging Democratic Sen. Patrick J. Leahy, had a primary opponent. Snelling, who served four terms as governor, easily defeated Anthony Doria, an educator who has run for the Senate twice and received less than 1 percent of the vote each time.

Gov. Madeleine M. Kunin (D) will face Republican Lt. Gov. Peter Smith and Burlington Mayor Bernard Sanders, a socialist who is running as an independent, on Nov. 4.

Wisconsin

Democratic senatorial primary candidate Edward R. Garvey defeated Matthew J. Flynn. Garvey had had a strong financial and organizational edge over Flynn, raising about $ 700,000 to Flynn's $ 150,000 and enjoyed the support of organized labor and much of the party establishment. Flynn, who was supported by Sen. William Proxmire (D-Wis.), proved to be an aggressive and tenacious opponent, however, calling Garvey a "special-interest puppet" of labor bosses. He also accused Garvey of hypocrisy for accepting political action committee (PAC) contributions while criticizing Sen. Robert W. Kasten Jr. (R-Wis.) for doing the same. Flynn refused PAC money, and Garvey responded that he needs it to be competitive with Kasten in November.

Kasten, who upset Sen. Gaylord Nelson (D-Wis.) in 1980, has a campaign war chest of about $ 2 million, including about $ 650,000 from PACs. Despite appearing vulnerable, partly because of a drunken driving charge in the District of Columbia last year, he has been effective in bringing federal grants to the state.

In the state's 7th Congressional District, Kevin Hermening, the youngest of 52 Americans held hostage at the U.S. Embassy in Iran during the 1979-81 crisis, won the Republican nomination. Hermening was a 19-year-old Marine stationed at the embassy at the time. He will face Rep. David R. Obey, who has represented the district for 17 years, on Nov. 4.