The 24-year-old Wheeler had given up four runs in consecutive losses to San Francisco and San Diego in his previous two starts before bouncing back in a big way against the struggling Marlins, who have dropped eight of 10.
Wheeler (3-7) struck out eight, yielding just three hits and a walk in guiding the Mets to a second straight win.
Wheeler, who made his debut with the Mets a year and one day ago, has owned the Marlins this season. In 21 innings, Miami has only managed to push one run across on nine hits.
David Wright provided the lone run for New York with a first-inning home run against Andrew Heaney (0-1), who was impressive in his major league debut for the Marlins. Heaney tossed six strong innings, allowing just the one run on four hits.
Widely considered Miami's top minor league prospect, Heaney compiled a 3-0 record with a 2.74 ERA in four starts with Triple-A New Orleans this season after an early promotion from Double-A.
Daniel Murphy had a pair of hits for the Mets.
Wright came up with the bases empty and two outs in the first inning and worked the count to 2-2 before welcoming Heaney to the big leagues with a blast to the monument in center field.
The young lefty settled down after that, getting Eric Campbell to pop out to shortstop to end the first inning and striking out two in the second.
Wheeler was never really threatened. He faced the minimum through eight innings, aided by a pair of double-play balls, before taking the mound for the ninth.
Jarrod Saltalamacchia, who had one of the three Miami hits, struck out swinging and Adeiny Hechavarria fouled out to first for the first two outs. Pinch-hitter Reed Johnson extended the game with a poke to left field, but Rafael Furcal ended it with a liner to center.