Cantu hit a two-run homer in the fourth inning, then lined a tiebreaking, three-run drive in the seventh.
Florida won minus All-Star shortstop Hanley Ramirez, who was hit by a pitch in the right hand the previous night. The Mets were missing first baseman Carlos Delgado and second baseman Luis Castillo, both nursing recent injuries.
Down 4-3 in the seventh, the Marlins rallied against Sean Green (0-1). Alfredo Amezaga drew a leadoff walk, Emilio Bonifacio chopped a one-out single to right and Cameron Maybin's slow groundout scored the tying run.
After a walk to John Baker, Cantu hit his fifth homer into the left-field seats. Cantu produced the seventh multihomer game of his career.
Burke Badenhop (1-0) pitched a scoreless sixth. Matt Lindstrom earned his fourth save in six chances - the former Mets prospect also saved the final game last year at Shea Stadium for Florida.
Whipping winds made every popup an adventure in the late innings, and Cantu was charged with an error when he misplayed one.
Dozens of hot-dog wrappers danced across the outfield as the night wore on.
The Mets held a pregame tribute to honor Gary Sheffield for hitting his 500th career home run earlier this season, and he quickly made a bid for No. 501.
With two runners on in the first, Sheffield launched a long drive to center - off the bat, the ball looked as if it had a chance to leave the park. Instead, it wound up short-hopping the wall beyond Maybin's reach near the 408-foot mark for a triple.
Sheffield slid in safely and then shot a glance at the wall, as if to wonder how the ball fell short. Through 11 games at Citi Field, the Mets have not hit a single home run between the power alleys. Overall, they've hit eight triples and only six homers at their new park.
Cantu's homer in the fourth off Livan Hernandez pulled Florida to 3-2. David Wright, booed after striking out his first two times up, delivered an RBI single in the Mets fifth off Ricky Nolasco.
Hernandez left in the sixth with one on, one out and Cantu coming up. Bobby Parnell relieved and after Cantu singled, the Marlins scored when John Baker hustled home from second as Jeremy Hermida's hard grounder to third bounced off Wright for an error.
Notes: Sheffield's two RBIs gave him 1,637, moving him past Ernie Banks into 26th place on the career list. ... Carlos Beltran extended his hitting streak to 11 games. ... Marlins manager Fredi Gonzalez said Ramirez is "50-50" to play in Wednesday's series finale.
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