After Alfredo Amezaga homered with two outs in the 12th off reliever Duaner Sanchez (1-0), the Mets rallied. Tatis' one-out hit came against Justin Miller (1-2).
The NL East-leading Marlins lost despite hitting four home runs, including two by Cody Ross. Mike Rabelo also homered.
Jose Reyes and Luis Castillo also homered for the Mets as they beat Florida for the second straight night
David Wright opened the bottom of the 12th with a walk from Miller, the seventh Marlins pitcher. Carlos Beltran followed with a single sending Wright to third.
After Miller struck out Damion Easley, Tatis doubled into the left-field corner and Beltran scored without a throw. Tatis had been 0-for-4 with a sacrifice fly before his game-winner.
Ross continued his remarkable month of May, hitting home runs in consecutive innings and driving in four runs as the Marlins built a 5-4 lead. The two homers gave Ross 11 hits this month, nine of them home runs.
Florida's bullpen protected the lead until Chavez connected against Kevin Gregg, who blew his second save in 12 chances. The Mets won for just the third time in 10 games.
Ross connected against Oliver Perez leading off the fifth. In the sixth, Perez walked Wes Helms with one out, Dan Uggla singled off Wright's glove at third base and Ross homered again.
Reyes opened the game for the Mets with a double, extending his hitting streak to 13 games. He then stole third and scored in front of Castillo's second home run of the season.
After Perez retired the first six Marlins, Rabelo led off the third inning with his second home run of the season.
The Mets got that run back in the fourth against Marlins starter Scott Olsen when Beltran led off with a double, moved to third on Easley's single and scored on Tatis' sacrifice fly.
Ross opened the fifth with a home run that pulled Florida within 3-2. Reyes restored the two-run lead for New York when he hit the first pitch in the bottom half for his seventh home run.
