However the results mirror earlier opinion polls that predicted a landslide win for Correa, a leftist candidate.
Final results are expected to be announced on Tuesday.
Correa, a US-trained economist and ally of Hugo Chavez, Venezuela's president, told supporters that we "accept this victory with dignity and humility".
At an earlier news conference in Quito, Correa said: "Thank God, we have triumphed. We are just instruments of the power of the people. This is a clear message that the people want change."
He said he would keep his promise to carry out widespread reforms which include re-negotiating debt agreements, opposing a US free-trade pact and re-writing the constitution.
"The people have given us a clear mandate, with the second largest margin in the last 30 years of democracy," he later told reporters in his tropical home city Guayaquil.
"We want a deep political reform."
However, Noboa, a billionaire banana magnate, rejected Sunday's early results, saying he would wait for the official count to end.
He said in a television interview: "I know in my interior that I won. The electoral tribunal will give the official figure once it has finished the vote count."
Correa won a place in Sunday's run-off by pledging a "citizens' revolution" against the discredited country's political system.
Ecuadoreans have driven the last three elected presidents from power and Correa appealed to voters as a fresh face in a field of established politicians.
He has pledged to construct 100,000 low-cost homes and copied Noboa's promise to double to $36 a "poverty bonus" that 1.2 million poor Ecuadoreans receive each month.
Correa's election would add another member to South America's grouping of left-leaning nations, which already includes Venezuela, Chile, Bolivia, Brazil, Argentina and Uruguay.