The election is being closely watched as a barometer of the political climate in Latin America, where more than a decade of leftist dominance has been waning.
It may also decide the fate of WikiLeaks founder Julian Assange, who has been holed up in Ecuador’s London embassy since 2012.
In a sign of the deep divisions in the South American oil producer, one of the two authorized exit polls gave Correa’s designated heir, Lenin Moreno, the edge.
The other said conservative ex-banker Guillermo Lasso would be the country’s next president.
“We will continue this process that has changed Ecuador’s reality, especially for the poorest citizens,” Moreno, a wheelchair user paralyzed in a 1998 carjacking, triumphantly told supporters.
“Starting today, Ecuador has a president who is going to promote national unity,” countered Lasso in a speech to his own supporters.
The confusion arose from contradictory exit polls from the companies contracted by state media, on the one hand, and private broadcasters, on the other.
Opinion Profiles, a firm some allege has government ties, gave Moreno 52 percent of the vote.
Cedatos, which the government calls an opposition polling firm, gave Lasso 53 percent.
The first official results are expected from 0100 GMT Monday.
Correa presided over an economic boom that has recently gone bust.
“It’s a decisive moment because we’ve had a conservative reaction in recent years,” the outgoing president said after casting his ballot, adding that “the whole world is watching.”
In Latin America, where a so-called “pink tide” of leftist leaders has been ebbing, the vote is seen as crucial.
Argentina, Brazil and Peru have all shifted to the right in recent months, as the region has sunk into recession and leftist leaders have been tarnished by a string of corruption scandals.
“I want a change and an end to corruption, once and for all,” said Elena Pabon, a 67-year-old retiree, as she went to the polls.
Fausto Dutan, 65, said he hopes “the good sense of our people prevails. I want the achievements of the past decade to keep taking hold.”
An opposition victory, he said, “would mean the collapse of this country.”
Boosted by high prices for its oil exports, Ecuador registered solid economic growth averaging 4.4 percent per year during the first eight years of Correa’s presidency, before tipping into recession in mid-2015.
Correa won loyal fans among the poor with generous social benefits that helped reduce the poverty rate from 36.7 percent to 23.3 percent in this country of 16 million people.
But he has also faced accusations of corruption and squandering the windfall of the oil boom.
Moreno, 64, won the first-round vote in February, with 39 percent to Lasso’s 28 percent.
But Lasso, 61, united the opposition vote behind his promises to create a million jobs and eliminate 14 different taxes.
Assange’s fate at stake
In another of the race’s hot issues, Lasso has threatened to revoke the political asylum Ecuador has granted its most famous guest, Assange.
Correa, an outspoken critic of the United States, let the WikiLeaks founder stay at the London embassy to avoid arrest and extradition to Sweden over rape allegations by two women.
The 45-year-old Australian, who denies the accusations, says he fears Sweden would send him to the United States to face trial for leaking hundreds of thousands of secret US military and diplomatic documents in 2010.
His case has returned to the spotlight since WikiLeaks was accused of meddling in the US election last year by releasing a damaging trove of hacked emails from presidential candidate Hillary Clinton’s campaign and her Democratic party.