The game featured seven home runs -- two of them by Florida's Cody Ross.
A solo shot by New York's Eddy Chavez in the ninth tied the game and the Marlins regained the lead in the 12th on a home run by Alfredo Amezaga, his first of the season.
Justin Miller (1-2) was then called upon in his first save opportunity of the year and he walked David Wright to open the Mets' 12th. Carlos Beltran singled Wright to third and Damion Easley then struck out.
That brought up Tatis, who doubled to left on Miller's first pitch, scoring both runners.
Despite giving up the 12th-inning homer to Amezaga, Duaner Sanchez (1-0) got the win. He worked the final two innings.
Ross hit a solo homer in the fifth, cutting Florida's deficit to 3-2, and added a three-run blast in the sixth that gave the Marlins' a 5-4 lead.
Swim Week Miami Beach 2014 [PHOTOS]