The election is already historic in Ecuador as the first in which an incumbent president has sought re-election.
Recent surveys show the socialist Correa with a wide enough edge
to meet Ecuador's constitutional standards to avoid a second-round election.
He would need to capture either a majority of the vote or a plurality of more than 40 per cent with a margin of at least 10 percentage points over the second-place candidate.
Correa has been polling at 48 to 51 per cent, with former president Lucio Gutierrez (2003-05) as the closest challenger, with no higher than 14 per cent.
Mariana Sanchez, Al Jazeera's correspondent in the capital Quito, said: "Correa has remained popular amongst most Ecuadorians throughout his presidency because he has invested millions of dollars to build roads and schools.
"He has even provided aid to poor single mothers with and $11 monthly bonus in cash," she said.
However, Sanchez said that Correa has lost some citizens' trust due to rising unemployment, and failing to pay foreign debt and consequently deterring foreign investment.
Since winning the presidency in November 2006, Correa has won three national votes, including a constitutional referendum.
The new constitution is the 20th since Ecuador was founded in 1830.
If Correa can finish off his challengers in Sunday's election, he will win a four-year term.
Under the new constitution, he would still be eligible to seek re-election to another four-year mandate.
Preliminary official results for the presidential election were expected to be issued late on Sunday, though broader results were likely to take longer, with 6,000 elected positions at stake.