With 40 per cent of the ballots counted late yesterday, Fujimori had 39 per cent of the vote, while former World Bank economist Pedro Kuczynski held 24 per cent.
Leftist congresswoman Veronika Mendoza, who had made a late surge in pre-election polls, was in third at 17 per cent.
Final results were not expected until sometime today, but Kuczynski's supporters celebrated in the streets outside his campaign headquarters in Lima after two unofficial quick counts indicated he would edge out Mendoza for the right to face Fujimori on June 5.
The centre-right Fujimori was the runaway front-runner for months and looked poised to outdo even the most-optimistic first round scenarios in polls published on the eve of voting.
But she will face an uphill battle in the second round because of how polarising a figure former President Fujimori remains among Peruvians.
While her father is remembered fondly by many, especially in the long-overlooked countryside, for defeating Maoist- inspired Shining Path rebels and taming hyperinflation, he is detested by large segments of the urban middle class for human rights abuses and his order for the military to shut down Congress.
In a bid to project a more moderate image, Fujimori promised during her campaign not to pardon her father, who is serving out a 25-year sentence for authorising death squads during his decade-long rule starting in 1990. Last night, she told supporters it was time to bury the past.
"Peruvians want reconciliation and don't want to fight anymore," she told supporters while standing on a truck parked outside a luxury Lima hotel.
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