BOSTON — Coming into Thursday night, the game was all about Cam Schlittler, but the hometown kid nearly got overshadowed by the Red Sox’ own hard-throwing young gun.

Until Payton Tolle left the game, when the Yankees pounced and Schlittler kept dominating.

Access the Yankees beat like never before

Join Post Sports+ for exciting subscriber-only features, including real-time texting with Greg Joyce about the inside buzz on the Yankees.

Cody Bellinger delivered the clutch hit — a pinch-hit, go-ahead, two-run single in the seventh inning — to make sure Schlittler’s strong night did not go to waste as the Yankees finished a sweep of the Red Sox with their sixth straight win, 4-2, at a sold-out Fenway Park.

Schlittler lacked the same swing-and-miss stuff Thursday that he showcased against the Red Sox in his AL wild-card series clincher last October — the showdown that sparked the social-media harassment toward him and his family, which continued through this rematch — but provided another memorable night nonetheless. The Walpole, Mass., native tossed a career-high eight innings while allowing just two runs (only one earned) and four hits while striking out five.

“He has that F-you attitude, like Carlos [Rodón] and Gerrit [Cole] that everybody loves and everybody adores when you’re playing behind him,” said Jazz Chisholm Jr., who hit his first home run of the year to tie the game 1-1 in the fifth. “So I think it’s pretty cool to see him go out there and do his thing, especially in his home city.”

The 25-year-old right-hander, who did not garner as much outward hostility from the crowd of 36,565 as expected, still rose to the occasion in what manager Aaron Boone described as “an ace-like performance” against the team he grew up rooting for.

In doing so, Schlittler became the latest Yankees starter to mow down an opponent, which has fueled their six-game winning streak.

“I didn’t think the emotions were too high,” Schlittler said. “It was a fun experience to come here, growing up around here, and being able to go throw. Great experience and just glad the boys got the sweep.”

David Bednar finished the win with a 1-2-3 ninth, completing a series in which the Red Sox (9-16) mustered just three runs and 13 hits.

“Wins are precious any time of year, especially within the division,” Boone said. “I know the Red Sox are scuffling a little bit to start the season right now, but we know they have a really good club and we know they’re going to get it going. So any time you can get wins against them, especially here, you take it.”

After Tolle exited with a 2-1 lead following six innings of one-run ball in which he struck out 11 — including punching out the first five batters — the Yankees (16-9) quickly took advantage, using a three-run seventh inning against the Red Sox bullpen to flip the game.

Trent Grisham, Chisholm and José Caballero strung consecutive one-out singles together to load the bases. Then with two outs, and righty reliever Greg Weissert entering the game, Bellinger pinch-hit for Amed Rosario and lined a two-run single the other way for the 3-2 lead.

Aaron Judge came up next and tacked on an insurance run with a single of his own, showing some extra emotion as he pumped his arms up and down toward the dugout.

And while Schlittler insisted it was “just another game,” it was clear his teammates wanted to make sure he came away with the win.

“Cam was doing Cam things,” Bellinger said. “He’s such a young kid. This rivalry is different when you wear these two uniforms. He’s just done a tremendous job pitching and handling everything that comes with it.”

Boston’s two runs came on a Marcelo Mayer double in the second inning — extended by a Rosario throwing error — and Carlos Narváez’s solo shot in the fifth, the first home run Schlittler allowed this season.

But he buckled down from there, making sure his homecoming ended with what mattered most.

“At the end of the day, I’m a competitor and I have a job to do,” Schlittler said. “Whether we’re in Boston or somewhere else, it doesn’t add more heat to that. I got to limit the distractions and go out there and do my job and help the team, put them in a spot to win the game.”