Public Advocate Bill de Blasio takes 15 percent support and 7 percent say they'd support Comptroller John Liu, while 1 percent support former Council member Sal Albanese and another 8 percent are undecided.
But New York election law provides for a runoff between the top-two vote-getters if no candidate is able to gain 40 percent of the vote in the primary. In that scenario, Thompson takes 52 percent to Weiner's 41 percent, and leads Quinn by nine points with 51 percent support.
Weiner would essentially tie Quinn in a runoff, taking 44 percent support to her 46 percent support.
Thompson has typically taken third place in most polls of the race, while Weiner and Quinn have traded first-place spots in various polls.
The survey was conducted from July 18-23, largely prior to the emergence of new details surrounding Weiner's illicit communications with a young girl who is not his wife.
Those details came out Tuesday, prompting Weiner to apologize to the public and his wife, and some of his opponents – including de Blasio and Albanese — to call for him to exit the race.
He's persisted, but were he to end his run, Quinn would take a slight lead, with 30 percent support to Thompson's 26 percent, while de Blasio would take 21 percent support and Liu would take 10 percent.
Weiner's lead comes despite the fact he's rated relatively poorly by Democratic voters in the new poll. Only 17 percent of those surveyed say having a strong moral character describes Weiner, while 57 percent say he has the right experience and 51 percent say he understands their needs.
The survey was conducted among 1,340 New York City registered voters and has a margin of error of plus or minus 2.7 percentage points. It includes 507 likely Democratic voters, and the Democratic portion of the poll has a margin of error of plus or minus 10 percentage points.