Harvey (1-0) -- appearing in his first major-league game -- allowed just three hits and three walks for the Mets, who won for just the second time in their last 14 games. He also stroked a double and a single in his first two at-bats.
The Mets grabbed an early lead when Scott Hairston drove in Ruben Tejada and Daniel Murphy with a first-inning double to right center -- one of three hits in the game for Hairston. Andres Torres came in on a fourth-inning sacrifice fly by Rob Johnson.
Tejada and Torres each had two hits and one run scored for the Mets.
Bobby Parnell issued two walks in the ninth but struck out Jason Kubel with runners on first and second in earning his third save.
Diamondbacks' starter Wade Miley (11-6) went 5 1/3 innings, allowing three runs on nine hits with three strikeouts and no walks.
Arizona has lost two straight after having put together a five-game winning streak.