The vote pits a left-wing teacher and populist political newcomer, Pedro Castillo, against a household name, right-winger Keiko Fujimori, the daughter of jailed ex-President Alberto Fujimori.
Uncertainty has gripped this country ahead of what polls have predicted will be a very close race.
Mr Castillo was the unexpected winner of the first round in April, which saw votes split among a wide field of candidates.
The teacher, who likes to campaign in a cowboy hat and often carries an oversized pencil – the symbol of his Free Peru party – won nearly 19% of the votes, followed by Ms Fujimori with 13.4%.
Since then, Mr Castillo has appeared to maintain an advantage, but the gap between the two has narrowed dramatically, with the most recent opinion polls suggesting a technical draw.
Deadly attack overshadowed campaign
In the countdown to the run-off, tensions in the electoral battle were exacerbated by violence on the ground.
On 23 May, an attack in central Peru killed 16 people, including four children. The armed forces blamed remnants of the Maoist Shining Path guerrilla group that has a bloody history in the country. Both Mr Castillo and Ms Fujimori condemned the attack.
