BOSTON — David Peterson earned his big boy pants Tuesday night, departing the mound in the sixth inning all grown up so quickly.

A major league debut can be scary enough, but for a left-handed pitcher performing in the Green Monster’s fabled shadow, the pressure can strangulate. And yet here was the 24-year-old Peterson in control against the Red Sox, perhaps quelling some concern about the Mets rotation.

Peterson mesmerized the opposition in leading the Mets to their second straight victory, 8-3 at Fenway Park.

“This is one of the greatest days of my life,” Peterson said. “This is something I’ve wanted to do since I was a little kid, and to go out there and make my first major league start, we got the win and I couldn’t have asked for much more.”

The defining inning for the left-hander was the third, when the Red Sox loaded the bases with nobody out, but scored only once on an odd double play that ended the frame. Overall, Peterson lasted 5 ²/₃ innings and allowed two earned runs on seven hits with three strikeouts and two walks, departing after 78 pitches. He became the first Mets starting pitcher to win his MLB debut since Steven Matz on June 28, 2015.

Drew Smith, Justin Wilson, Dellin Betances and Hunter Strickland combined for 3 ¹/₃ innings in relief. The Mets and Red Sox are now headed to Citi Field for two games that begin Wednesday night.

Peterson, the Mets’ first-round pick in the 2017 draft (he was originally selected by the Red Sox three years earlier in the 28th round, but opted to pitch at Oregon), wasn’t officially told until Tuesday morning that he would be filling the spot in the rotation vacated by Marcus Stroman, who last week was placed on the injured list with a left calf tear. The Mets became familiar with Peterson in spring training and summer camp this year and were impressed with his poise.

“Right now with David included and our other four starters, that was similar to the performance that any of our starters can give us right there,” manager Luis Rojas said. “Just a solid outing by him.”

After Kevin Plawecki doubled to left field over J.D. Davis’ outstretched glove to begin the third, Peterson walked Andrew Benintendi and Jose Peraza’s single off Brandon Nimmo’s glove loaded the bases. Peterson dug in, striking out J.D. Martinez before Rafael Devers hit a line drive that Robinson Cano trapped and flipped to second for the out. Plawecki scored on the play and Benintendi was eventually tagged out in a rundown between second and third.

“I felt really good in the bullpen and I felt confident in my stuff,” Peterson said. “I felt like I went out there and four weapons to go against the Red Sox with and it was just all about keeping them on their toes and not letting them get comfortable in the box.”

Davis gave the Mets a 5-1 lead in the fifth with his first homer of the season, a slicing two-run shot off the Pesky Pole in right field. A night earlier, Davis appeared to get robbed of his first homer, as a replay showed his shot to left field cleared the Green Monster in fair territory. The Mets never challenged the foul ball ruling.

The Mets scored three runs in the second inning without particularly hard contact against lefty Matt Hall. In the inning Cano delivered an opposite-field RBI double after Davis had singled leading off and Yoenis Cespedes was hit by a pitch. Nimmo walked to load the bases and Amed Rosario’s bloop two-run single gave the Mets a 3-0 lead.

Peterson received a gift right from the start: Peraza hit a shot off the Green Monster leading off the game for the Red Sox, but was thrown out by Davis attempting to reach second. In the second inning, Michael Conforto reached over the low fence that juts into the right-field foul line to catch Michael Chavis’ pop up.

“That is a tough lineup to navigate a couple of times, three times and this kid maintained his poise,” Rojas said. “He mixed different sequences … the uptick in velocity he has been displaying since his first camp is playing a great role for him and the rest of his pitches right now.”