Wheeler (2-5) struck out nine and allowed just one run on Marlon Byrd's homer. He yielded four hits and did not walk a batter over 6 1/3 innings as the Mets opened a season-long 11-game road trip with their fourth win in five games.
David Buchanan (1-1), who was making his second career start, surrendered four runs -- three earned -- on seven hits over 6 2/3 innings to take the loss.
The Mets opened the second inning with three consecutive singles, two of which never left the infield, and they pushed a run across when Travis d'Arnaud bounced into a 6-4-3 double play.
Young, who hit .086 (3-for-35) over his previous 14 games, took Buchanan deep in the fourth, and New York added another run in the fifth, again with only one ball reaching the outfield.
A single, error and botched fielder's choice loaded the bases, and Curtis Granderson took a payoff pitch off the plate to force in a run.
Wheeler struck out the side in the first two innings and retired 14 in a row before Byrd homered off him in the seventh.
Scott Rice and Vic Black finished off the seventh, Black stayed on and pitched a 1-2-3 eighth, and Jenrry Mejia struck out all three batters he faced in the ninth to post his fifth save.
Swim Week Miami Beach 2014 [PHOTOS]