The two candidates are at opposite ends of the political spectrum - a fact that has worried some Peruvians who say they will not vote for either of them.
Opinion polls indicate that the outcome is too close to call.
The two candidates led the field after the first round on 10 April, which saw the defeat of three centrist candidates. No-one gained more than the 50% needed to win the election outright.
Whoever wins Sunday's vote will succeed Alan Garcia, who cannot stand for a second term.
Spoiled ballots
Keiko Fujimori, 36, appeals to voters who still admire her father, president for a decade from 1990. He is now serving a 25-year jail sentence for corruption and organising death squads.
She has defended his record, saying by taming hyper-inflation and defeating Marxist Shining Path rebels, he laid the basis for Peru's current economic boom.
She supports free-market economic policies, advocates a tough approach to crime and has promised to improve social programmes and infrastructure in poor areas.
Critics say her main aim is to secure a pardon for her father, a claim she denies.
If she wins, she would become Peru's first woman president.
Ollanta Humala, 48, comes from a left-wing tradition of greater state intervention. He staged a short-lived rebellion against Alberto Fujimori in 2000 and narrowly lost to Alan Garcia in the last presidential election in 2006.
He has campaigned on a promise to increase the state's role in the economy and redistribute wealth to Peru's poor majority.
His critics fear he will embark on interventionist policies similar to those of Hugo Chavez in Venezuela, although Mr Humala says he is more in sympathy with Brazil's moderate left-wing approach.
He has also denied allegations that he committed human rights abuses during the fight against Shining Path rebels in the 1990s when he was an army captain.
Polls suggest that around 10% of Peru's voters could abstain or spoil their ballots, Reuters news agency reports.
Peruvian painter Fernando de Szyszlo is one of those. "It really pains me not to vote, but I'm not voting," he told the Associated Press.
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