Maybe the Yankees have stopped the bleeding — and they have the Mets, in part, to thank.

The Yankees swept the Mets in The Bronx, winning their third straight overall with a 4-2 victory on Tuesday in front of another sellout crowd of 49,217.

And it came with plenty of tension, as Wandy Peralta got Francisco Lindor to fly to center with the bases loaded to end it.

“It’s been a tough stretch and these wins can go a long way for us to get our swagger back,’’ manager Aaron Boone said, as the Yankees kept their AL East lead over Tampa Bay at eight games, while the Mets saw their lead over Atlanta shrink to two games in the NL East.

The Mets were down by two runs with two outs in the ninth, when pinch-hitter Tyler Naquin drew a walk against Clarke Schmidt, who had thrown three scoreless innings out of the bullpen.

Brandon Nimmo then reached on an infield single and Starling Marte walked to load the bases and knock Schmidt out of the game.

Peralta came in and Lindor nearly tied it with a liner to left, but it landed foul.

Lindor followed with the fly ball to center.

“I understand the game was on the line and I’ve just got to execute,’’ Peralta said through an interpreter.

Schmidt put it more bluntly: “Wandy came in and saved my ass.”

The series, in front of two electric crowds, made the teams want more.

“I think about it, because that’s as close to a playoff atmosphere as you’re gonna get,’’ Aaron Judge, who hit his 48th home run, said of whether an October Subway Series was on his mind. “This and at Citi Field. You look ahead at the pace we’re on and what they’re on too. But we’ve got to get there first.”

The Yankees went ahead on Andrew Benintendi’s run-scoring single in the seventh.

After the Mets had tied the game in the top of sixth, Oswaldo Cabrera led off the seventh with a single up the middle and Isiah Kiner-Falefa bunted him to second.

Pinch-hitter Jose Trevino popped one down the right-field line, which Pete Alonso misplayed into a single.

Benintendi then delivered a single to left to put the Yankees ahead again and Judge belted a two-out RBI single to make it 4-2.

Schmidt walked Lindor and gave up a single to Alonso to start the eighth, but got Daniel Vogelbach to ground into a double play. With Lindor on third, Jeff McNeil lined out to right.

Frankie Montas had his best start as a Yankee, giving up two runs in 5 ²/₃ innings, and the Yankees finally got to Taijuan Walker in the fourth inning after the Mets right-hander retired the first nine batters he faced in his first start since leaving his previous outing in Atlanta on Aug. 16 with back spasms.

Montas got through a 27-pitch first inning without allowing a run and pitched out of trouble again in the second — helped by a nice double play turned by Kiner-Falefa and Gleyber Torres.

Montas then retired eight straight, including five strikeouts in a row.

DJ LeMahieu grounded into a double play in the fourth inning before Judge crushed a 3-2 pitch high into the left-field bleachers, a 453-foot, 115 mph shot that gave the Yankees a 1-0 lead.

Cabrera drew a bases-loaded walk to make it 2-0.

Mark Canha drilled a double to the wall in right-center in the fifth and Brett Baty reached on a catcher’s interference before Tomas Nido bunted both runners over for the top of the order.

With two outs, Marte singled to right to score Canha, but Baty was also sent and thrown out at home by Cabrera — playing just his second game in right — to preserve the Yankees’ one-run lead, thanks also to a good tag from Kyle Higashioka.

The Mets tied it on a wild play in the sixth. With Alonso on first, McNeil doubled to right-center. Alonso should have scored easily, but stumbled around third base and stopped between third and home. McNeil was also caught between second and third on the play, but the crowd noise prevented Torres from knowing Alonso had tripped and he didn’t throw home.

Instead, he raced McNeil to second, but McNeil beat him, allowing Alonso to score.