Duaner Sanchez gave up a tying homer to Mike Jacobs in the eighth, setting the stage for Heilman's collapse in the ninth.
New York's NL East lead was trimmed to one game by Philadelphia, which beat the Chicago Cubs 5-2 on Saturday.
The Marlins avoided slipping to .500 for the first time since they were 3-3. On Sunday, they'll try for their first two-game winning streak this month.
Heilman (3-8) started the ninth by walking Hanley Ramirez, who advanced on a sacrifice and took third on a wild pitch. Jorge Cantu and Mike Jacobs were intentionally walked to load the bases, and Willingham earned a game-ending walk when he took a 3-1 pitch that was inside.
Matt Lindstrom (2-2) retired Damion Easley and Jose Reyes with a runner on second to end the top of the ninth.
David Wright hit a two-run homer for the Mets, his 26th.
Pelfrey was seeking his third consecutive complete game but left with two on in the seventh. Sanchez struck out Cantu to end the inning but gave up Jacobs' 27th homer leading off the eighth.
Florida's Ricky Nolasco struck out eight but gave up three runs in six innings.
The teams cleared the benches in the second inning after Pelfrey hit Cody Ross on the arm with a pitch.
Ross slammed his protective gear to the ground as he walked to first base, then shouted profanities at Pelfrey. When the players took a couple of steps toward each other, both benches emptied.
No punches were thrown, and no one was ejected. Pelfrey picked off Ross to end the inning.
Luis Castillo singled and Wright homered to give New York a 2-0 lead in the first. Reyes hit his 17th triple in the third and came home on Castillo's single.
Pelfrey had been 0-3 with a 10.66 ERA in three starts this season against the Marlins, but they failed to score against him until the sixth. After he retired the first two batters in the inning, Cantu and Jacobs singled, Willingham walked and Dan Uggla hit a two-run single.
Notes: Uggla improved to 9-for-18 (.500) this season with the bases loaded. ... In his past seven starts, Nolasco has struck out 59 and walked four. ... Wright is 10-for-22 (.455) against Nolasco with three home runs.
