The survey from pollster Analogias put support for Massa, the outgoing government's economy chief, at about 42% versus 34% for Milei, a combative self-described anarco-capitalist.
Political polling has been wildly off in Argentina in recent years, including ahead of last Sunday's first-round vote, when Milei led in nearly all polls but ultimately came in second to Massa by about six points.
The Analogias poll, one of the first to estimate support for the Nov. 19 run-off, follows Wednesday's shakeup when Milei won the key endorsement of last Sunday's third-place finisher, conservative Patricia Bullrich, who attracted almost a quarter of the vote.
Bullrich's support for Milei should help him win over some of her more moderate conservative voter base that is opposed to the ruling Peronists, though her own coalition is deeply divided about backing the radical libertarian.
The new poll also shows nearly 18% undecided in the head-to-head match-up, while about another 6% said they will vote for no one.
Nearly 2,000 voters were surveyed from Oct. 23-35 for the survey.
It also estimates Massa is winning about a third of those who supported last Sunday's fourth-place finisher, as well as almost 15% of those who opted for Bullrich.
A couple other polls released this week showed mixed results, with one from CB Consultora giving Milei slightly more than a 1% lead over Massa, but another by Proyeccion Consultoras putting Massa ahead by about 10 points.
The run-off campaign takes place at a time of severe economic crisis in South America's second-biggest economy, with consumer prices surging by triple digits and the local currency steadily plummeting in value.
This article was produced by Reuters news agency. It has not been edited by Global South World.