Moreno, a disabled former vice president, needs 40 percent of valid votes and a 10-percentage-point difference with his nearest rival to win outright and extend a decade of left-wing rule in the Andean country.
He had 38.26 per cent of votes versus 29.86 per cent for Lasso, according to the electoral council with 51.8 per cent of ballots counted.
Moreno, who lost the use of his legs two decades ago after being shot during a robbery, has a more conciliatory style than pugnacious President Rafael Correa and has promised benefits for the disabled, single mothers and the elderly.
"Nothing and no one can stop this revolution," said Moreno, flanked by Correa, as the first exit polls came out.
"We've won these elections fair and square."
The socialist presidential candidate favors continuing to grant the Australian whistleblower asylum, which was granted to him under outgoing leader Rafael Correa.
Cheering supporters in Quito waved Ecuadorean flags as well as green ones proclaiming "Lenin" next to Moreno's face.
But Lasso expressed confidence he would make it to a second round. "We will present ourselves to the Ecuadorean people once again," he said in his hometown of Guayaquil near the Pacific Coast.
Lasso has campaigned on a platform to revive the economy - which is dependent on exports of oil, flowers and shrimp - by slashing taxes, fostering foreign investment and creating 1 million jobs in four years.
Should there be a second round, Ecuador's fragmented opposition is expected to coalesce around Lasso amid anger over an economic downturn and corruption scandals.
Argentina, Brazil, and Peru have moved toward the right recently as a commodities boom ended and weakened a leftist bloc in the region rich in oil, metals and soy.
Correa, one of the key figures in Latin America's leftist axis for years, has brought stability to the politically turbulent country but has aggravated many with his confrontational style. He plans to move to Belgium with his Belgian wife after leaving office.
