Nieuwenhuis was recalled from Triple-A Las Vegas prior to the game to replace outfielder Juan Lagares on the active roster.
The Mets placed Lagares on the 15-day disabled list with a pulled right hamstring. New York was also without right fielder Curtis Granderson, who is considered day-to-day after running into the fence, injuring his rib and forearm in Monday's win.
Eric Young collected three hits with two RBI and two runs scored and Andrew Brown also knocked in two RBI starting in place of Granderson.
New York starter Jenrry Mejia (2-0) went five innings and allowed just two hits with three strikeouts and two walks to earn the win. Mejia was cruising through the Diamondbacks order, but was taken out of the game after five scoreless frames because of a blister on his throwing hand.
Gonzalez Germen pitched three scoreless innings in relief and Kyle Farnsworth pitched a perfect ninth as Mets pitching held the Diamondbacks to just three hits. New York has won three of its last four.
Bronson Arroyo (1-1) was roughed up for nine runs on 10 hits over 3 1/3 innings for Arizona, which has lost five straight. His ERA rocketed up to 9.95 over three starts this season.
New York opened the game with three straight hits to load the bases. Lucas Duda then grounded into a force out that scored Young.
Brown followed with a deep sacrifice fly to center that plated Daniel Murphy. Nieuwenhuis knocked in Duda with a single up the middle in his first at-bat of the season.
The Mets tacked on a crooked number in the top of the fourth when Nieuwenhuis crushed a two-run homer to right which increased the cushion to 5-0.
Arroyo then walked Travis d'Arnaud before Omar Quintanilla doubled to center. Mejia followed with a weak fly to left for the first out of the inning, then Young and Murphy each hit singles to make it an 8-0 game. Young knocked in two with his hit and scored all the way from first when Murphy's basehit was misplayed by A.J. Pollock in center.
Arroyo was chased shortly thereafter and Randall Delgado came on in relief, immediately loading the bases by hitting Duda. Brown grounded into a force out that plated Murphy and the Mets led 9-0 after 3 1/2 frames.
Gerardo Parra walked to lead off the home half of the fourth which was the first baserunner for Arizona. Paul Goldschmidt then ripped a single down the third-base line two batters later for the Diamondbacks' first hit of the night. Parra and Goldschmidt, however, were stranded on base as the fourth came to a close.