Fujimori, a four-time presidential hopeful and the daughter of former president Alberto Fujimori, now has 50.11 per cent of the votes, putting her ahead of leftist rival Roberto Sanchez by 43,386 votes.
Only 40,213 potential votes remain to be counted, according to data from Peru's ONPE electoral authority late on Tuesday.
The electoral authority has yet to officially declare a winner and plans to do so in mid-July.
Fujimori's expected victory deepens Latin America's rightward shift, following outsider Abelardo De La Espriella's election in Colombia on Sunday.
Voters concerned about crime have flocked to hardline candidates.
Earlier on Tuesday, Sanchez alleged that "fraud was under way", without providing evidence, and said he would refuse to recognise the results of the election, raising the prospect of a prolonged political crisis in Peru.
Sanchez had requested the annulment of thousands of votes cast abroad that mostly favoured Fujimori, but Peru's national electoral jury rejected the request on Tuesday night.
The run-off results had been delayed by a review of contested ballots, the late arrival of ballots from abroad and the razor-thin difference between candidates.
Fujimori is set to inherit a country that has seen eight presidents in as many years and which is grappling with stark economic inequalities between the capital and rural regions as well as disillusionment with politicians.
Of the eight former presidents, none completed a full term, with three impeached and one resigning after just six days.
Four former presidents are currently in prison, and Fujimori's late father served 16 years over human rights abuses during his decade-long rule in the 1990s.
Fujimori, who previously distanced herself from her father's legacy, has leaned into it this election - casting herself as a strong leader best able to enforce order and stability as voters grapple with rising rates of extortion and murder.
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