Rep. Clarence J. Brown (R-Ohio), making his first bid for statewide office after 17 years in the House, won a surprisingly easy victory over Seth Taft, the grandson of a former president, in the Ohio Republican gubernatorial primary last night.

But it was unclear whom he will face next fall as the lead in the hard-fought Democratic primary seesawed between state Attorney General William Brown and former lieutenant governor Richard F. Celeste in the early morning hours.

With 88 percent of the votes counted Celeste led Brown 42 to 37 percent. Former Cincinnati mayor Jerry Springer, who late in the campaign broadcast ads in which he admitted a liaison with a prostitute, was a distant third.

Taft, the early front-runner in the Republican race, battled ultra-conservative state Sen. Thomas A. Van Meter for second place as returns trickled in. Each had about 20 percent of the vote, compared with Brown's 54 percent. Taft, a former Cuyahoga County commissioner, in a concession speech credited Brown with putting together a "superior statewide organization."

With an unemployment rate of 12 percent in the state, Brown is expected to face an uphill battle in his attempt to replace retiring Gov. James A. Rhodes.

Voters also picked gubernatorial nominees in Maine, South Carolina and Iowa. In Iowa Roxanne Conlin won the Democratic gubernatorial nomination, and in Arkansas former Democratic governor Bill Clinton won his runoff race against former attorney general Joe Purcell.

Republican nominees were picked to run against incumbent Democratic Sens. Quentin N. Burdick of North Dakota, John Melcher of Montana and George J. Mitchell of Maine.

Sen. Howard M. Metzenbaum (D-Ohio), seeking a second term, easily won renomination over a token opponent, Norbert Dennerll, an anti-busing activist. In November Metzenbaum will face state Sen. Paul Pfiefer, a moderate who overcame a late-developing conservative write-in challenge in the GOP primary.

With 98 percent of the precincts reporting, Rep. Ronald M. Mottl (D-Ohio), who angered local party leaders by supporting President Reagan's economic policies, was virtually tied with Cuyahoga County Commissioner Edward Feighan in a bitterly fought congressional district in the Cleveland suburbs. Feighan had a lead of only about 850 votes.

The Republican race was between two of the state's best known political names, Taft and Brown, who holds the same congressional seat his father first won in 1938.

In primary voting yesterday:

Iowa

Conservative Lt. Gov. Terry Branstad was unopposed for the GOP nomination to succeed popular longtime Gov. Robert D. Ray, one of four Midwest Republican governors not seeking reelection this year.

Conlin, a liberal former U.S. attorney and a feminist leader and organizer who is attempting to become Iowa's first woman governor, defeated former lieutenant governor Jerome Fitzgerald of Fort Dodge, who ran unsuccessfully against Ray in 1978, and former state Democratic chairman Ed Campbell of Des Moines. With 26 percent of the vote counted Fitzgerald and Campbell conceded; Conlin had 43 percent of the vote, Fitzgerald 34 percent and Campbell 23 percent.

South Carolina

Democratic Gov. Richard W. Riley was unopposed for renomination, and is favored to win reelection next fall. William Workman, retired editor of The State, Columbia's morning newspaper, defeated Roddy Martin, an electronics expert, for the GOP nomination.

Arkansas

Clinton, seeking to resurrect a once-promising political career, defeated Purcell in the Democratic runoff for the right to challenge GOP Gov. Frank White.

With 95 percent of the vote counted, Clinton led Purcell, 54 percent to 46 percent. A former Rhodes Scholar who was ousted by White in 1980 after one term in office, Clinton, 35, appealed to the voters to give him a "second chance" at his old post. "We had the issues on our side," he told supporters last night.

Maine

Democratic Gov. Joseph E. Brennan, 47, of Augusta, was nominated for a second term, overcoming a token challenge from state Rep. Georgette Berube of Lewiston.

In the Republican gubernatorial primary, lawyer Charles Cragin, who ran unsuccessfully in 1978, won a closely bunched three-way race against state Rep. Sherry F. Huber, a wealthy pro-choice abortion activist, and state Sen. Richard Pierce.

With 88 percent of the precincts reporting, Cragin, a lobbyist for medical interests and a leader of a tax-indexing referendum drive last year, had 37 percent of the vote to 32 percent for Huber and 31 percent for Pierce.

In the Senate primaries, Democrat Sen. George J. Mitchell, who was appointed in 1980 to fill the unexpired term of former senator Edmund S. Muskie, was nominated without oppositon. His Republican opponent in the fall will be Rep. David F. Emery of Augusta, who also had no primary opposition.

Montana

Democratic Sen. John Melcher easily won his bid for renomination to a second term over Michael A. Bond, a businessman and environmental activist. Melcher, who had been attacked last year by the National Conservative Political Action Committee (NCPAC) for his liberal voting record, came under fire from Bond for being too moderate.

On the Republican side, Larry Williams, an investment counselor, easily defeated lawyer Willie Morris.

North Dakota

Both parties already had made their major decisions by conventions, so the primary was a formality.

Democratic Sen. Quentin N. Burdick and Democratic Rep. Byron L. Dorgan were unopposed.

On the Republican side Gene Knorr, 41, a Minot rancher and former U.S. Treasury official, was nominated to challenge Burdick in the fall for the Senate seat. The GOP's House candidate will be Kent Jones, 55, the agriculture commissioner.