PRI candidate Enrique Pena Nieto had significant poll support over the third-place PAN Party's Josefina Vazquez Mota, who is trying to become the country's first female leader, The New York Times reported.
Former Mexico City Mayor Andres Manuel Lopez Obrador, the candidate of the leftist Party of the Democratic Revolution, ranked second in polls this week.
The PRI ruled Mexico for 70 years and developed a reputation for corruption and graft, the Times said. They were voted out in 2000 and PAN member Vicente Fox became president. Fellow PAN member Felipe Calderon succeeded him.
The Times said the global recession, the North American Free Trade Agreement and burgeoning crime has dogged voters' patience and downwardly affected incomes.
Census figures show 57 percent of Mexican workers earn less than $13.50 per day.
The polls were to be open for 12 hours across the country's four time zones.