The result marks the former US president's biggest defeat as he attempts to play kingmaker before November's midterm elections.
And Georgia Secretary of State Brad Raffensperger also weathered Mr Trump's bid to oust him over his and Mr Kemp's refusal to try to overturn the former president's defeat in the 2020 election.
Mr Trump had backed Mr Perdue, who repeatedly promoted his claims that he lost in 2020 due to widespread voter fraud, Reuters reported.
Edison Research had predicted a win for Mr Kemp, who held a commanding 73-23 per cent lead over Mr Perdue.
Mr Kemp will face Stacey Abrams, a progressive who secured the Democratic nomination on Tuesday.
He beat Ms Abrams in 2018 and sought to paint her as a far-left radical who only viewed the governor's role as a “stepping stone” to the White House.
“Our battle is far from over,” Mr Kemp said. He thanked Mr Perdue for pledging his support.
“Tonight the fight for the soul of our state begins to make sure that Stacey Abrams is not going to be our governor or the next president.”
But the night was not a total loss for Mr Trump.
His pick for US Senate, former American football star Herschel Walker, easily won the Republican nomination and will now face Democratic US senator Raphael Warnock on November 8.
In Texas, the Trump-backed attorney general Ken Paxton defeated state land commissioner George P Bush in a run-off after the March primary.
The political environment has grown increasingly favourable to Republicans in the run-up to November's midterms.
A Reuters/Ipsos opinion poll completed on Tuesday showed President Joe Biden's approval rating has fallen to 36 per cent, the lowest level of his presidency, reflecting voter concerns over rising inflation.
Republicans are favoured to win a majority in the US House of Representatives in November, although analysts say Democrats have a better chance of holding on to control of the Senate.
The loss of either chamber would bring Mr Biden's legislative agenda to a halt and give Republicans the power to launch distracting and potentially politically damaging investigations.
Mr Raffensperger, who rejected a plea by Trump in 2020 to “find” enough votes to alter the outcome, beat back Representative Jody Hice, whom Mr Trump endorsed, to win a second term as the main arbiter of elections in Georgia.
Ms Hice frequently echoed the former president's baseless voter fraud claims.
Mr Trump has made more than 190 endorsements since leaving office, mostly for incumbent Republicans who face no serious primary opposition.
He has amassed a mixed record in competitive contests. His nominee for US Senate in Pennsylvania, the television host Dr Mehmet Oz, is in a race still too close to call a week after voting.
Four other states — Alabama, Texas, Arkansas and Minnesota — also held primary elections on Tuesday.
In Alabama, US Representative Mo Brooks, who lost Mr Trump's endorsement after saying it was time to move on from the 2020 election, was among those battling for a Senate seat.
Trump-era White House spokeswoman Sarah Huckabee Sanders won the Republican nomination for governor in Arkansas, Edison predicted.
In Texas, US Representative Henry Cuellar, a moderate Democrat, was locked in a tight run-off with progressive challenger Jessica Cisneros.
Mr Cuellar boldly declared victory right before midnight but Ms Cisneros, refused to concede, as the race was separated by less than 200 votes.
Elsewhere in Georgia, Lucy McBath beat Carolyn Bourdeaux in rare a contest pitting two incumbent Democratic US representatives against one another after Republicans redrew the state's congressional map.