Pete Alonso might not love the days he serves as the Mets’ designated hitter, but the role certainly has agreed with him so far in its first year of existence in the National League.

Alonso belted his third home run of the season — all coming in his three starts as a DH — to help the Mets to a chilly 5-0 win Sunday over the Diamondbacks at Citi Field.

“I just try to stay as locked in as I possibly can, watching video and do whatever I can to keep my body warm,” Alonso said. “Today was a little more difficult because of the cold conditions, and I had to move around and stay active … and as engaged in the game as possible.”

Before the game, Buck Showalter said he’d informed Alonso and explained the rationale of his plan to have Dominic Smith man first base in the series finale.

“I told him, ‘Understand, I’m trying to figure out a way to have you play 150-160 [games], a lot of games for us. This is designed to have you available to us as much as possible,’ ” Showalter said. “Pete’s our first baseman, he’s going to play the majority of our games at first base, but when we DH him, it’s designed to keep him on the field for the long haul.”

Alonso ripped his only two previous home runs this season with nine RBIs over two starts at designated hitter, April 9 at Washington and Wednesday in Philadelphia. Alonso’s two-run blast to left-center in Sunday’s seventh inning against Arizona righty Matt Peacock extended the Mets’ lead to 5-0.

Meanwhile, even the No. 7 starter on the Mets’ depth chart is throwing nothing but zeroes, as David Peterson lasted 4 ¹/₃ scoreless innings in place of injured starter Taijuan Walker. Despite also being without ace Jacob deGrom (shoulder), the starting staff’s ERA was lowered to a league-best 1.07.

“You see the other guys do well and you want to do well,” Peterson said. “We’d love to have Jake in the rotation, he’s one of the best in the game. But it’s next man up and when he’s ready to rejoin us, even better.”

Trevor Williams, Chasen Shreve (two innings), Drew Smith and Edwin Diaz combined to record the final 14 outs to complete the pitching staff’s third combined shutout already through the team’s 7-3 start ahead of a four-game series beginning Monday against the Giants.

“Seven and three, that’s what it is, that’s the facts, that’s what happened,” Alonso said. “We’ve been playing really good team baseball, and today was a great example of that.

“For us, there’s only one way and we’re coming right at you.”

Peterson didn’t make the Opening Day roster, but the lefty allowed no runs on three hits with two walks and four strikeouts before Showalter pulled him for Williams after 80 pitches with one down in the fifth. Peterson also had tossed four scoreless innings in relief of Walker (shoulder) in Philadelphia last Monday.

Still, the Mets managed only one hit against Arizona starter Humberto Castellanos through his four scoreless innings, a single to left by James McCann in the third.

The Mets maintained the scoreless knot in the sixth. The inning began with Starling Marte turning a catchable ball into a sun-aided double for the second time in the game. Shreve relieved Williams and retired the side, however, stranding Christian Walker at third.

The Mets were aggressive on the bases and cashed in on some shoddy Arizona defense in the bottom half to break through for the first three runs of the game. Diamondbacks right-fielder Pavin Smith overthrew second base on Eduardo Escobar’s one-out double, enabling Alonso to score.

Pinch-hitter J.D. Davis added an RBI single against 40-year-old former Mets lefty Oliver Perez before McCann made it 3-0 with a sacrifice fly to left.

“It was awesome. I think if we don’t press the issue there, we don’t score those runs,” Alonso said. “Eddie busting out of the box right after contact and him hustling the whole way forced the defense to try to make a play. I feel like our aggression there paid off on the base paths.”