The Marlins were leading 3-0 in the eighth but the Mets rallied for three runs -- including a run scored on a wild pitch uncorked by Heath Bell -- forcing extra innings.
In the 11th, Reyes (3-for-5, two runs scored) led off with a three-bagger against Collin McHugh (0-4).
After the Mets issued two intentional walks to load the bases, McHugh struck out Rob Brantly but Donovan Solano then sent a bouncer up the middle for the game-winning RBI.
Chad Gaudin (4-2) earned the victory with a scoreless top of the 11th for the Marlins, who clinched their season-ending three-game series.
Gorkys Hernandez socked a solo homer in the win.
Scott Hairston went 4-for-5 with an RBI for the Mets.
Swim Week Miami Beach 2014 [PHOTOS]