Brian Kemp trounces Trump-backed David Perdue in a Republican primary battle for Georgia governor.

ATLANTA — In a landslide victory that represented a resounding rebuke of Donald J. Trump, Gov. Brian Kemp of Georgia won the Republican nomination for a second term on Tuesday, turning back a Trump-fueled primary challenge and delivering the former president his biggest electoral setback of the 2022 primaries.

Mr. Trump had made defeating Mr. Kemp and his allies a top priority, seeking retribution for the decision by the governor and secretary of state, Brad Raffensperger, to certify the 2020 election in Georgia. After his subversion efforts were rebuffed, Mr. Trump personally recruited former Senator David Perdue to run for governor and his endorsement against Mr. Raffensperger was one of the earliest of his post-presidency.

Both Mr. Kemp and Mr. Raffensperger won anyway — and Mr. Kemp was leading by roughly 50 percentage points with more than 90 percent of the vote counted, a blowout that easily avoided a runoff.

Mr. Perdue had anchored his candidacy on promoting falsehoods about fraud in the last election, blaming Mr. Kemp both for Mr. Trump’s defeat and for his own loss in a 2021 runoff that gave Democrats control of the Senate. Mr. Trump went all in for Mr. Perdue: working to clear the field for him, recording television ads, holding a rally and even transferring $2.64 million from his political accounts to help him.

The lopsided outcome exposed the limits of Mr. Trump’s hold on his party’s base, marking the third consecutive week a candidate he had backed for governor had lost. It also was a sign of the waning potency of Mr. Trump’s obsession with relitigating his 2020 loss two years later.

Chris Christie, the former governor of New Jersey and a onetime Trump adviser, who had campaigned with Mr. Kemp, celebrated on Twitter, declaring that voters had rejected “the DJT Vendetta Tour.”

The victory for Mr. Kemp, 58, sets up a rematch of his 2018 battle with Stacey Abrams, 48, who won the Democratic nomination unopposed on Tuesday, in what will be one of the most closely watched governor’s races in the nation this fall. His most urgent imperative is reuniting a Republican Party fractured by the divisive primary.

Standing on the artificial turf of a football field inside the Chick-fil-A College Football Hall of Fame in downtown Atlanta, Mr. Kemp refused to rhetorically spike the football. He thanked his opponent “for the spirited debate” and said Mr. Perdue had endorsed him in a phone call.

In a moment that underscored the bitterness of the race, Mr. Perdue said in a short concession speech in Atlanta that “everything I said about Brian Kemp was true” while still urging his backers to rally against Ms. Abrams, calling Mr. Kemp a “much better choice.”

While Georgia received top billing on Tuesday, several other states held primaries, including Texas, where a mass shooting at an elementary school left at least 19 children dead and a nation in mourning. Mr. Kemp had delayed his victory speech until after President Biden addressed the tragedy from the White House.

In Georgia’s U.S. Senate race, Herschel Walker, the former University of Georgia football star who was also recruited by Mr. Trump, won the Republican nomination and will face Senator Raphael Warnock, a Democrat, in November. The matchup in the fall, the outcome of which could tip control of the Senate, is a rare general election contest in the South pitting two Black candidates against one another.

While Mr. Walker glided through the primary, his tumultuous past — including accusations of domestic abuse and his exaggerated and false claims about his business success — is expected to receive a more thorough airing in the general election.

Both parties expect Mr. Walker to be the subject of coming commercials questioning his competence and credentials. His Democratic opponent, Mr. Warnock, 52, one of the best fund-raisers in the nation, has been on the television airwaves for months already, focusing largely on positive messages.

With nearly 200 endorsements so far, Mr. Trump has set up the 2022 primary season as a rolling referendum on his influence in the party. He has scored notable big successes, such as J.D. Vance in Ohio, and suffered defeats in Nebraska and Idaho. But no state so far has been as much a focus for Mr. Trump as Georgia, where he not only set out to oust the governor but also Mr. Kemp’s allies across other statewide offices.

Mr. Trump’s pick for attorney general lost in a landslide and his choice for insurance commissioner was far behind, as well. His choice for the open lieutenant governor’s office was ahead but possibly headed to a runoff.

In the secretary of state race, Mr. Raffensperger, the Republican incumbent whom Mr. Trump pressured to “find” the sufficient votes to overturn the election in early 2021, averted a runoff against Representative Jody Hice, leading by roughly 200,000 votes early Wednesday morning.

The secretary of state serves as Georgia’s top elections official, and the winner in the fall will have great sway over how the 2024 presidential campaign will be conducted in a key battleground state.

Representative Marjorie Taylor Greene of Georgia, the right-wing firebrand, handily cast aside a more moderate challenger, carrying more than two-thirds of the vote in her district.

In Texas, the last scion of the Bush political dynasty, Land Commissioner George P. Bush, was defeated in the state attorney general’s race, losing to the scandal-plagued incumbent, Ken Paxton. And in a Democratic contest along the border, Representative Henry Cuellar, one of the most moderate Democrats in the House, was deadlocked against a progressive challenge from Jessica Cisneros that has drawn national attention.

In Alabama, three Republican candidates had vied to make the runoff to succeed retiring Senator Richard Shelby: Representative Mo Brooks; Mike Durant, the helicopter pilot portrayed in “Black Hawk Down”; and Katie Britt, a former chief of staff to Mr. Shelby. Mr. Trump had initially endorsed Mr. Brooks early in 2021, but as Mr. Brooks sagged in the polls, he rescinded that endorsement. Mr. Brooks advanced to the runoff with Ms. Britt, who was the top vote-getter.

Gov. Kay Ivey of Alabama won her primary against two right-wing challengers.

And in Arkansas, Sarah Huckabee Sanders, the former White House press secretary and the daughter of former Gov. Mike Huckabee, easily won the Republican primary for governor. Senator John Boozman of Arkansas avoided a runoff against Jake Bequette, a former football star, in a race that has seen more than $7 million in television ads.

In Georgia, Mr. Kemp had methodically locked up the support of the state’s biggest political players and donors in anticipation of a Trump-led primary battle. He signed into law numerous conservative priorities, including a restrictive new voting law in 2021 and a gas-tax holiday that extends just past the primary. He also expanded gun rights, raised teacher pay and dispatched tax rebate checks that went out in recent weeks.

All those maneuvers and more left Mr. Perdue isolated, with little to lean on beyond the support of Mr. Trump, who has seethed for 18 months about Mr. Kemp’s refusal to attempt to overturn the 2020 election results in his state.

“His endorsement is still important, but it comes with an asterisk,” said Stephen Lawson, a Georgia-based Republican strategist, adding that the Perdue campaign’s failure was “proof positive your message has to be more than that.”

Even before the election was over, Mr. Perdue’s own allies began openly criticizing the Perdue effort as lackluster. And many national Republicans rallied behind Mr. Kemp, as the Republican Governors Association took the unusual step of intervening to spend more than $5 million on ads in the primary. Ambitious potential 2024 Republican presidential candidates campaigned for him, including Mr. Christie and, on the eve of the election, former Vice President Mike Pence.

Despite Mr. Trump’s ire and public attacks, Mr. Kemp never fired back at the former president. “I’ve never said anything bad about him,” Mr. Kemp said on Monday. “I don’t plan on doing that. I’m not mad at him. I think he’s just mad at me.”

Now Mr. Kemp must hope that discipline pays off and that Mr. Trump — who mused at a rally in Georgia last fall that Ms. Abrams “might be better than having your existing governor” — does not actively work to torpedo him in November.

Mr. Walker tried to stay neutral in the governor’s primary, declining to endorse or even say who he was voting for. The 60-year-old political newcomer avoided any debates during the primary and mostly ignored his rivals in a field that included Georgia’s agriculture secretary, Gary Black.

Mr. Black had warned repeatedly that the untested Mr. Walker would prove unelectable — “he’ll never win,” Mr. Black said in a recent interview — and that Republicans would come to regret his anointment.

One of the ways Mr. Trump attempted to ease the path for Mr. Perdue was to push another ally, Vernon Jones, out of the governor’s race and into an open congressional contest. That race was headed to a runoff.

Georgia Republicans redrew district lines ahead of 2022, cramming two House Democrats into the same suburban Atlanta district and diluting the Democratic strength of another seat in the state’s southwestern corner held by Representative Sanford Bishop. Mr. Bishop, a Democrat, faces his first serious challenge in years this fall.

As a result, Republicans could grow their share of the congressional delegation from 8-6 to 10-4.

In the primary that placed two Democratic incumbents against each other, Representative Lucy McBath beat Representative Carolyn Bourdeaux on Tuesday.

Richard Fausset contributed reporting.