The Braves took a one-half game lead over San Diego, which lost 1-0 to Chicago, for the wild card.
Philadelphia's 8-0 win earlier in the evening eliminated Atlanta in the NL East.
The Braves had lost five of their previous six games, scoring a total of nine runs in that span. They barely scored enough to win this time at Turner Field, where they have the best home record in the majors at 53-23.
Nate McLouth opened the 11th with a walk and moved up on a sacrifice by Alex Gonzalez. Rick Ankiel walked and both runners moved up on a wild pitch. Pinch-hitter Freddie Freeman struck out before Infante hit a 3-2 pitch from Jose Veras (3-3) down the left-field line.
Mike Dunn (2-0) picked up the win getting the final out in the 11th after Peter Moylan got the first two.
The Braves had a chance to win it in the ninth but Jason Heyward bounced out weakly to pitcher Brian Sanches with the bases loaded and two outs.
The Marlins tied it at 1 on a double in the seventh by Brad Davis that scored Mike Stanton, who had singled and stolen second off Braves starter Tommy Hanson.
Hanson allowed five hits, no walks, and struck out three in 7 2-3 innings. He had pitched 15 scoreless innings before Florida's run.
The Braves led 1-0 on a solo home run by Brian McCann in the fourth inning off Alex Sanabia. It was his 21st.
Sanabia pitched seven innings and gave up five hits, didn't walk a batter and struck out five in the game delayed 1 hour, 6 minutes by rain.
Notes: Atlanta RHP Jair Jurrjens, out since his last start on Sept.14 with a right knee injury, took some anti-inflammatory medication before the game. If that doesn't work, he'll have another MRI exam. He is likely to miss the rest of the regular season. ... Braves 3B Martin Prado sustained a left hip pointer while swinging at a pitch in the fifth inning and left the game. He was listed as day to day. ... The Braves will start Tim Hudson on Tuesday night and Derek Lowe on Wednesday, both on three days' rest. ... Florida SS Hanley Ramirez did not start for the sixth straight game because of a sore left elbow. He said Monday night his right elbow hurts, too. He pinch ran in the eighth.
(This version CORRECTS Braves 2, Marlins 1. Corrects Braves' lead to one-half game.)