Representative samples from polling stations throughout the country gave Peña Nieto the lead, with between 37.93% and 38.55% of votes, the Federal Election Institute said.
The projected victory for Peña Nieto marks a triumphant return to power for the PRI, which controlled Mexico's presidency for more than 70 years, until the election of the National Action Party's Vicente Fox in 2000.
Criticisms of Peña Nieto and concerns about the PRI's possible return to power have fueled a student movement that has staged protests throughout the country in recent weeks.
But the charismatic 45-year-old former governor has also galvanized fervent support among residents of his home state and party loyalists nationwide.
The frontrunner's campaign platform includes plans to stop the rise in food prices, promote energy reform, give social security to all Mexicans and reduce violence nationwide.
The Consulta Mitofsky, GEA/ISA and Parametria firms also said their exit poll results projected a win for Peña Nieto, with more than 40% of voters saying they cast ballots for the PRI candidate.
In addition to Peña Nieto, three other candidates were vying for the presidency in what officials called "the largest and most complex election day" in the country's history.
Ruling party candidate Josefina Vazquez Mota was trailing in exit polls.
Throughout the three-month campaign, she appeared to be distancing herself from President Felipe Calderon. Her campaign slogan was "Josefina Diferente."
But at a campaign rally Wednesday night, the National Action Party (PAN) candidate praised the "valor" of Calderon's fight against organized crime and made a surprise announcement that she would invite him to be Mexico's attorney general if she wins the presidency.
As preliminary results trickled in Sunday night, Vazquez Mota acknowledged that the trend did not appear to be in her favor.
Andres Manuel Lopez Obrador of the Democratic Revolution Party (PRD) ranked in second place in numerous polls leading up to the election. Sunday night's quick count indicated that he had received between 30.9% and 31.86% of votes.
In the 2006 presidential vote, election authorities said the former Mexico City mayor narrowly lost to Calderon. Lopez Obrador claimed election fraud and never conceded, referring to himself as "the legitimate president of Mexico."
His supporters protested nationwide. In Mexico City, they staged sit-ins and blockades.
On Wednesday, Lopez Obrador told throngs of supporters in Mexico's capital that he was confident that he would "win the presidency again."
Gabriel Quadri of the New Alliance, who lagged far behind in polls before and after the election, praised Mexico's election authorities Sunday night.
"We have very solid, democratic institutions," he said.
In polling centers throughout the country, workers began the day Sunday assembling cardboard voting booths marked with bold black letters saying, "The vote is free and secret."
But some voters said they were afraid of fraud.