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J.D. Vance, the author of “Hillbilly Elegy,” won a G.O.P. race that saw nearly $80 million in television advertising. The author and venture capitalist parlayed an endorsement from Donald J. Trump into victory, beating out a crowded field of conservative challengers.Maddie McGarvey for The New York TimesCINCINNATI — J.D. Vance, the author whose memoir, “Hillbilly Elegy,” about life in Appalachia became a best seller, decisively won the Ohio Senate primary on Tuesday after a late endorsement by Donald J. Trump helped him surge past his rivals in a crowded primary field.Casting himself as a fighter against the nation’s elites, Mr. Vance ran as a Trump-style pugilist and outsider who railed against the threats of drugs, Democrats and illegal immigration, while thoroughly backpedaling from his past criticisms of the former president.The contest, which saw nearly $80 million in television advertising, was one of the most anticipated of the 2022 primary season for its potential to provide an early signal of the direction of the Republican Party.The result delivered a strong affirmation of Mr. Trump’s continued grip on his party’s base. But a fuller assessment of Mr. Trump’s sway will come through a series of primaries in the next four weeks — in West Virginia, North Carolina, Idaho, Pennsylvania and Georgia.Mr. Vance had been trailing in most polls behind Josh Mandel, a former Ohio state treasurer who had also aggressively pursued Mr. Trump’s backing, until the former president’s mid-April endorsement helped vault Mr. Vance ahead. A third candidate, State Senator Matt Dolan, ran as a more traditional Republican, sometimes mocking his rivals for their unrelenting focus on the former president instead of Ohio issues and voters.Cheers went up at Mr. Vance’s Cincinnati election party when The Associated Press called the race shortly after 9:30 p.m.“The people who are caught between the corrupt political class of the left and the right, they need a voice,” Mr. Vance said in his victory speech. “They need a representative. And that’s going to be me.”Mr. Vance is an unlikely champion of the Trumpian mantle, after calling the former president “reprehensible” in 2016 and even “cultural heroin.” But he had changed his tune entirely by 2022, and Mr. Trump called to congratulate him on his victory on Tuesday evening, according to a person briefed on the call.With more than 80 percent of the vote counted, Mr. Vance was leading across almost the entire state. But the results also captured some of the tensions and demographic trade-offs of a Republican Party pulled in different directions as Mr. Dolan was strongest in the voter-rich cities of Cleveland and Columbus.Trump-style Republicans did not prevail in the other top contest on Tuesday. Gov. Mike DeWine of Ohio, a more traditional Republican who has held offices in the state for more than 40 years, finished far ahead of his multiple primary rivals after a strong right-wing challenge never gained traction despite some conservative backlash to Mr. DeWine’s early and assertive response to the coronavirus pandemic.Gov. Mike DeWine and his wife, Fran DeWine, greet their daughter Anna Bolton and grandson Calvin after voting in Cedarville, Ohio, on Tuesday.Paul Vernon/Associated PressMr. DeWine had almost double the votes of his closest rival, Jim Renacci, a former House member. In the fall, he will be running against Nan Whaley, the former mayor of Dayton, who won the Democratic nomination on Tuesday, becoming the first woman in Ohio history to be nominated by a major party for governor.In the Senate race, Mr. Vance will now face Representative Tim Ryan, a 48-year-old Democrat from the Youngstown area who has positioned himself as a champion of blue-collar values and has not aligned with some of his party’s more progressive positions.If Mr. Vance prevails in the fall, the 37-year-old graduate of Yale Law School and investor would become the second-youngest member of the Senate, the chamber’s youngest Republican and a rare freshman who would arrive in Washington with a national profile.Mr. Vance’s metamorphosis from an outspoken “Never Trump” Republican in 2016 to a full-throated Make America Great Again warrior in 2022 echoes the ideological journey of much of the party in recent years. Republicans have moved closer and closer to the former president’s hard-line policy positions on issues like trade and immigration, and to his combative posture with Democrats and on cultural issues that divide the two parties. For some Republican voters, the primary was animated by fears that traditional family values and a white American culture were under attack by far-left Democrats, establishment Republicans and elites.Mr. Vance also won the endorsements of some of the Make America Great Again movement’s loudest firebrands, including Representatives Marjorie Taylor Greene of Georgia and Matt Gaetz of Florida, both of whom campaigned with him in the race’s final weekend, and Donald Trump Jr., who also traveled to the state. He also had a crucial financial benefactor: His former boss, Peter Thiel, the Silicon Valley investor who pledged $10 million to Mr. Vance even before he joined the contest and who added millions more in the final stretch to trumpet Mr. Trump’s endorsement.The Senate primary was unusual in the extent that it unfolded in two places at once. In Ohio, there was the typical fevered competition for votes, in town halls, debates and television ads. In Florida, there was the battle for Mr. Trump’s approval at Mar-a-Lago, the former president’s private club, with public shows of fealty, lobbying by surrogates and shuttle diplomacy. In one episode last year, multiple Ohio candidates vied for Mr. Trump’s support in front of one another at an impromptu meeting at Mar-a-Lago.In a verbal flub that seemed almost fitting to how the candidates ran, Mr. Trump accidentally conjoined the names of two rivals over the weekend. “We’ve endorsed J.P., right?” Mr. Trump said at a rally in Nebraska. “J.D. Mandel.”Mr. Trump’s endorsement set off a frenzy among Ohio Republicans who questioned Mr. Vance’s Republican credentials, with rivals circulating fliers online and at a Trump rally accusing him of being a Democrat in disguise and resurrecting his past comments against Mr. Trump.The Senate candidate Josh Mandel, center, with supporters, including Senator Ted Cruz of Texas, left, in Columbus, Ohio, last week.Joshua A. Bickel/The Columbus Dispatch, via Associated PressMr. Mandel had been the front-runner for much of the race, casting himself as the true pro-Trump candidate (“Pro-God. Pro-Guns. Pro-Trump” was the tagline in his TV ads). But that became an all-but-impossible argument to prosecute in the final weeks after Mr. Trump picked Mr. Vance.“If the whole issue in the campaign is who is most Trump-like, expect it to work against you when you don’t get the endorsement,” said Rex Elsass, an Ohio-based Republican strategist.At a restaurant in the Cleveland suburb of Beachwood on Tuesday, more than a dozen Mandel supporters and campaign volunteers struck an optimistic tone at the start of the night, expressing confidence. But it was not too long before Mr. Mandel took the podium to deliver the news. Mr. Mandel told the crowd that he called Mr. Vance “to congratulate him on a hard-fought victory” and would do what he could to help get him elected. “The stakes are too high for this country to not support the nominee,” Mr. Mandel said to a round of applause in the room.Beyond Mr. Vance, Mr. Dolan and Mr. Mandel, the crowded race included a single female candidate, Jane Timken, a former Ohio Republican Party chair, who was backed by the retiring incumbent, Senator Rob Portman, as well as Mike Gibbons, a businessman who poured millions of his own money into the race and at one point had vaulted to the top of the polls.Mr. Dolan had toiled for most of the contest far behind the polling leaders, avoiding direct attacks from his rivals. But he tapped into his own fortune to fund more than $11 million in television ads as he cut a path separate from the rest of the Trump-focused field by refusing to amplify the falsehood that the 2020 election was rigged. At one debate, Mr. Dolan was the lone candidate to raise his hand to say the former president should stop talking about the 2020 election.State Senator Matt Dolan greets supporters at a library opening in Bay Village, Ohio, last week.Dustin Franz for The New York TimesThe contest was nasty and lengthy, with nothing capturing the intensity more than a near-physical confrontation between Mr. Gibbons and Mr. Mandel at one March debate, where they bumped bellies as they lobbed verbal threats at one another.Mr. Vance scolded them both. “Sit down. Come on,” he said. “This is ridiculous.”Much of the race was shaped by huge sums spent on television — nearly $80 million, according to the ad-tracking firm AdImpact, with a lot of it coming from outside groups and out-of-state donors. The conservative Club for Growth spent more than $12 million on television ads aimed to boost Mr. Mandel or tear down his rivals. Mr. Thiel, the Silicon Valley investor, seeded a pro-Vance super PAC with $10 million in early 2021 — months before Mr. Vance even entered the race. Mr. Vance is one of two former Thiel employees — the other is Blake Masters in Arizona — running for Senate with Mr. Thiel’s hefty financial backing. Mr. Thiel had served as a key link between Mr. Vance and Mr. Trump, attending an introductory meeting between them in early 2021. The politics of Ohio have changed drastically in the Trump era. Once the quintessential presidential swing state, Ohio broke for Mr. Trump by 8 percentage points in both 2016 and 2020, ending a half-century streak of the state backing the national winner. Republicans have sharply run up their margins among working-class white voters and in more rural areas, offsetting the losses that the party has suffered in the state’s suburbs around cities like Columbus and Cleveland.Representative Tim Ryan, right, with Michael S. Regan of the Environmental Protection Agency in Youngstown, Ohio, where lead pipes will be replaced as part of new federal infrastructure spending.Dustin Franz for The New York TimesIn the Democratic primary, Mr. Ryan, who briefly ran for president in 2020, easily turned back a primary challenge from Morgan Harper, 38, a former adviser at the Consumer Financial Protection Bureau who ran as a progressive, banking $5 million for the general election.Mr. Ryan has already run an anti-China ad that focuses on Ohio jobs and his opening ad of the general election has him tossing darts inside a bar and seeking to separate himself from the broader Democratic brand, lamenting those who have called for defunding the police.But Mr. Ryan faces an uphill race in a state that has trended Republican and in a year when his party is saddled with President Biden’s low approval ratings. Some Republicans see Mr. Ryan as formidable — Mr. Trump among them — but the general election is not seen by either party as among the half-dozen closest contests that will determine control of the Senate, now divided evenly 50-50.Shane Goldmacher reported from Cincinnati. Jazmine Ulloa reported from Beachwood, Ohio. More