Wheeler knocked in Miguel Montero with a one-out RBI double in the second inning, breaking a 1-1 tie, and then scored on the first of Parra's two run-producing hits.
Montero bashed a two-run homer in the fourth to give Arizona a 5-2 lead and the D-backs went on to take a 2-1 lead in their four-game series against New York.
Ian Kennedy (9-8) earned the victory after allowing three runs on seven hits over 6 1/3 innings, striking out nine.
Mets starter Chris Young (2-5) was lit up for six runs on seven hits in a four-inning effort.
Ike Davis went 4-for-4 with three solo homers for the Mets, who lost for the ninth time in 11 games.
Notable deaths of 2014 [PHOTOS]