Glenn Youngkin, a wealthy first-time candidate who walked a line between his party’s Trump-centric base and appeals to business interests, won the Republican nomination for governor of Virginia on Monday. He heads into a general election in one of only two states choosing their governors in 2021, in the latest running of an off-year race often viewed as a referendum on the party holding the White House.

Late Monday, Mr. Youngkin’s last remaining rival, Pete Snyder, conceded the race. “I send my heartfelt congratulations,” Mr. Snyder wrote on Twitter. “He + the ticket have my 100% support.”

The results were tabulated by Republican officials two days after roughly 30,000 voters cast ranked-choice ballots at 39 locations around the state. Mr. Snyder conceded after more than 12 hours of vote counting, in which five candidates were knocked from contention, one by one, and their supporters’ next-choice votes were allocated to others still in the running. In the sixth round of counting, Mr. Youngkin passed the required 50 percent threshold.

The unusual nominating process came after an internal party squabble in which Republicans rejected holding a traditional primary, which would have drawn a larger and more diverse group of voters. Former Republican officials from an era before the party fell hard from power in Virginia criticized the nominating process as likely to increase the G.O.P.’s marginalization.

But neither of the two candidates who most closely aligned themselves with former President Donald J. Trump — who did not endorse anyone — prevailed, raising Republican hopes for the November election.

Mr. Youngkin will face the winner of the Democratic primary next month. In that race, former Gov. Terry McAuliffe has held a significant lead in fund-raising as well as in recent polls over four rivals.