The election could also decide the fate of WikiLeaks founder Julian Assange, who has been holed up at the country's London embassy since 2012.
Correa presided over an economic boom that has recently gone bust in the South American oil producer. With voters torn between continuity and change, the race remains too close to call.
The runoff pits the socialist president's designated heir, Lenin Moreno, against conservative ex-banker Guillermo Lasso.
The race is also a barometer of the political climate in Latin America, where more than a decade of leftist dominance has been waning.
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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.
Boosted by high prices for its oil exports, Ecuador registered solid economic growth of 4.4 per cent per year on average during the first eight years of Correa's presidency, before tipping into recession in mid-2015.
But he has also faced accusations of corruption and squandering the windfall of the oil boom.
Political analyst Napoleon Saltos of the Central University of Ecuador said the election would be played out between "the vote against the government and the fear among certain parts of the population that they will lose what they gained over the past 10 years."
Lasso, 61, appears to have gained the edge by uniting the opposition vote behind his promises to end tax-and-spend policies and create a million jobs.
"We're heading for a change, yes, but a positive change, not a negative change, a change toward the past," he told AFP on Wednesday.
In another of the race's hot debates, 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 Assange stay at the embassy to avoid arrest and extradition to Sweden over a rape allegation.
The 45-year-old Australian, who denies the accusation, 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.
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