The Mets placed center fielder Juan Lagares, their leading hitter, on the 15-day disabled list with a pulled hamstring and called up Nieuwenhuis from the minors before the game. He slid into Lagares' spot nicely, hitting a two-run homer during a six-run fourth inning against Bronson Arroyo (1-1) and adding a diving catch in the fifth.
Mejia (2-0) was sharp before leaving with a torn blister. Eric Young Jr. had three hits and two RBIs, and the Mets finished with 12 hits to ensure a winning record on their nine-game road trip.
The Diamondbacks had another awful night on the mound, losing their seventh straight home game and eighth in nine at Chase Field.
Arroyo allowed 10 runs in less than four innings and Arizona has given up 38 through the first five games of a homestand that ends Wednesday against the Mets.
Mejia struggled with walks during his first two starts — nine in 11 innings — but was hitting his spots against the Diamondbacks. He was perfect through three innings and didn't allow a hit until Paul Goldschmidt sneaked a single inside third base with one out in the fourth.
Mejia escaped a jam in the fifth inning and got some defensive help from Nieuwenhuis, who made a sliding catch in center to rob Mark Trumbo of a hit.
Mejia tore a blister on his right index finger and didn't come out for the sixth after allowing two hits. Gonzalez Germen allowed a hit in three innings and Kyle Farnsworth closed out the shutout with a perfect ninth.
Arroyo got an extra day of rest between starts, but it didn't seem to do him much good.
New York jumped on him from the start, stringing together three straight singles and scoring three runs in the first inning. Nieuwenhuis capped the outburst with a run-scoring single up the middle.
It got much worse for Arroyo in the fourth.
Nieuwenhuis added his pool-deck homer to right-center and Young followed with a two-run single to left. New York scored another run on a single and error by center fielder A.J. Pollock and went up 9-0 on Andrew Brown's fielder's choice.
Arroyo allowed 10 runs and nine hits in 3 1-3 innings.
About the only thing that went right for the Diamondbacks came in the fifth inning when manager Kirk Gibson challenged a close play at first and had it overturned on replay — with the score 9-0. Mejia got two weak groundouts with two on to end the inning.
NOTES: Mets RF Curtis Granderson was out of the lineup after he injured his left forearm and ribs colliding with the outfield wall Monday night. He is day to day. ... Arizona's Miguel Montero went 0 for 4 to end a five-game hitting streak. ... New York's David Wright extended his hitting streak to seven games with a single in the fourth. ... Arizona RHP Brandon McCarthy, scheduled to start Wednesday, has a 1.16 ERA in four starts against NL East teams. ... Mets RHP Dillon Gee, who will start Wednesday, allowed four earned runs in five innings in his only start at Chase Field.