ATLANTA — Gov. Brian Kemp of Georgia easily dispatched with Donald Trump’s hand-picked challenger on Tuesday in a Republican primary that demonstrated the limits of the former president and his conspiracy-fueled politics in a critical swing state.

Kemp will face Democrat Stacey Abrams this fall in what will be one of the nation’s most consequential governor’s races.

The results served as a stinging rebuke of Trump in a race that he prioritized above almost all others. Angered by Kemp’s refusal to go along with his extraordinary effort to overturn the 2020 election results in Georgia, Trump personally recruited former Sen. David Perdue to launch a primary. Trump even encouraged another Republican to drop out of the race to clear a path for a Perdue victory.

But Kemp ultimately emerged as a powerful candidate able to draw prolific fundraising totals that helped him flood Georgia with television and other ads. He tapped into the power of his office to show voters what he could do for them, unveiling a $5.5 billion, 8,100-job Hyundai Motor plant near Savannah in the final days of the campaign.

“Even in the middle of a tough primary, conservatives across our state didn’t listen to the noise. They didn’t get distracted,” Kemp told cheering supporters, before calling on his party to rally behind his campaign.

In defeat, Perdue struck a unifying tone that has become increasingly rare in a Republican Party dominated by Trump’s hardline tactics.

“I want you to know tonight that I am fully supporting Brian Kemp in his run to beat Stacey Abrams,” Perdue said. “It’s emotional for all of us, we’re disappointed, I get that. Let’s take a few hours, lick our wounds, and tomorrow morning, you’re going to hear me going to work for Brian Kemp to make damn sure that Stacey Abrams is never governor of Georgia.”

In all, five states were voting Tuesday, including Alabama, Arkansas, Texas and Minnesota. But none had been more consumed than Georgia by Trump and his lie that the 2020 election was stolen.

Perdue’s loss becomes the latest example of a primary setback for Trump’s preferred candidates, who have lost governor’s races in Idaho and Nebraska. A Pennsylvania Senate primary is too close to call a week after the election.

Still, the totality of Tuesday’s contests underscored the sustained power of Trumpism in Republican politics 18 months after he was voted out of office. His preferred Senate candidate in Georgia, Herschel Walker, easily won the GOP nomination despite warnings from Walker’s Republican competitors about his history of domestic violence and mental health struggles. He will face Democratic incumbent Sen. Raphael Warnock in the fall in a race that could determine control of the chamber.

Georgia Secretary of State Brad Raffensberger, who refused to support the former president’s direct calls to overturn the 2020 election, was in a fight to avoid what could be a challenging runoff election. Raffensperger faces three primary challengers, including Trump-backed Rep. Jody Hice. The winner will serve as Georgia’s chief election officer in the 2024 presidential election.

And former Trump White House press secretary Sarah Sanders, who was the face of an administration that contributed to the nation’s stark divide, won the Republican governor’s nomination in Arkansas.

Regardless of Trump’s involvement in their races, virtually all of the Republican candidates — even Kemp — ran on “election integrity.” That phrase that has emerged as a code for the former president’s baseless grievances about the 2020 election, which were roundly rejected by courts and his own attorney general.