Pre-election surveys gave Correa about 55 percent, with the closest of his seven rivals, the wealthy conservative banker Guillermo Lasso, trailing at between 9 to 15 percent.
A candidate wins the presidency if he gets over half the votes, or at least 40 percent with at least a 10-point lead over the second-placed candidate.
Sunday's poll opened at 7 a.m. (1200 GMT), with closing scheduled at 5 p.m, local time. Media were due to release exit surveys shortly after voting ends, with authorities releasing initial official results two hours later.
Voters will also select Ecuador's National Assembly and five representatives to the regional Andean Parliament. In the National Assembly Correa's Alianza Pais party was aiming for an absolute majority. It currently has 42 percent.
The 49-year-old Correa had used his final campaign rally on Thursday to appeal to supporters "to defeat the conspirators at the ballot box and make the citizens' revolution irreversible."
Ecuador leads Latin America in social spending, with his government citing increased access to education and health, the building or improvement of 7,820 kilometers (4,870 miles) of highways, and the creation of 95,400 jobs over four years.
Lasso, in turn, promised to encourage investment, lower taxes on job-creating companies and to roll back what Correa has termed "21st century socialism."
Correa drew world attention last year by granting asylum to Julian Assange at the Ecuadorean Embassy in London when the WikiLeaks founder was sought by Sweden on sexual assault accusations.
The president also counts among his advisers the hacker Kevin Mitnick, an American who did five years in prison for hacking into US telecommunications systems.
Correa, a graduate of the US University of Illinois-Champaign, challenged big business and media, imposed new contracts on oil companies and renegotiated Ecuador's debt while touting poverty reduction.
Critics cite infringements
Correa's critics, however, including human rights groups, say he wields a near-monopoly on power against anyone who threatens his "citizens' revolution."
He tackled the opposition, alienated the church and used libel law to try to silence journalists. Critics say he stacked courts with friendly judges and prosecuted indigenous leaders for protesting Correa's opening up of Ecuador to mining firms without their consent.
The president accuses media of backing a police revolt in 2010 and has barred ministers from talking with opposition newspapers.
Though he presents himself as a "defender of freedom of expression," Correa wants to enact new media regulations. Critics say Correa scares capital away and point to alliances with the left-wing Cuban and Venezuelan leaders, Fidel Castro and Hugo Chavez.
Ecuador, population 15 million, has 11.6 million registered voters, and anyone 18 to 65 is required to participate in elections. The government dispatched more than 30,000 military personnel and 20,000 police officers on Sunday to keep the peace.
About 320 observers from the Organization of American States, the United States, Russia and India were monitoring polling.
Ecuador had five presidents between 1997 and 2007.
mkg/ipj (AFP, Reuters, dpa, AP)