The survey conducted by Ipsos Apoyo and published in El Comercio newspaper says Humala, who has moderated his once fiery left-wing discourse, has 42 percent support. Fujimori got 36 percent in the poll.
Humala and Fujimori won 31.7 percent and 23.6 percent of the vote respectively in the first round on April 10.
They face each other in a final round of voting on June 5.
"In the weeks ahead both candidates will have to go out and win the support of the 22 percent of voters that have not decided in favor of either of them," Alfredo Torres, head of Ipsos Apoyo, told El Comercio.
The poll of 1,802 voters was taken in April 16-21 and had a margin of error of 2.3 percentage points.
Fujimori is running as a business-friendly candidate and is most popular among women voters and well-to-do residents of capital city Lima, Torres said.
She is largely trusted by international investors, but many voters associate her with the corruption and human right crimes that sent her father to prison.
Investors remain uncertain about Humala, who in 2006 ran for president with the support of Venezuela's outspoken left-wing leader Hugo Chavez.
This month, Humala appointed experience technocrats to his campaign team in a bid to convince the markets that he would keep much of Peru's market economy intact if elected.
Humala is most popular among poor, rural voters and men over the age of 25, Torres said.
Despite a decade-long boom, a third of Peruvians still live in poverty. Many have rallied behind Humala, a former army officer turned populist politician who says he can close the country's gaping social inequalities.