The Marlins began the night four games behind Colorado in the National League wild card chase.
Florida, which had won its previous two games, came back from an early three-run deficit and owned a 5-4 advantage going into the ninth.
Leo Nunez (4-5) came on in search of his 24th save, but promptly loaded the bases on singles by Daniel Murphy and Jeff Francoeur along with a walk to pinch-hitter Jeremy Reed.
Sullivan then hit for Anderson Hernandez and stroked an 0-1 pitch into left field for his two-run single. The Mets again loaded the bases with one away, but could do no more damage.
Bobby Parnell (4-8) got the win by working the eighth inning. Francisco Rodriguez pitched the bottom of the ninth for his 34th save.
The Mets snapped a three-game losing streak.
Both sides had three-run homers -- Francoeur for the Mets in the second and Hanley Ramirez for the Marlins in the fifth.
Copyright 2009 by United Press International.