One of the reasons the Yankees traded for J.A. Happ was the lefty’s success against the Red Sox.

And he proved how good he is against the Yankees’ rivals again in Tuesday’s 3-2 win over Boston in The Bronx, when Happ gave up just an unearned run in six innings.

But Happ has pitched well enough that he has to be under serious consideration to face the A’s in the nearly inevitable AL wild-card game the Yankees would have to win to get to face Boston in the ALDS.

Happ has faced the Red Sox three times this season and allowed just one earned run — although he gave up five unearned runs in 3 ²/₃ innings at Fenway Park on July 12 while still with Toronto. His 2.82 ERA against the Red Sox is Happ’s lowest against any AL team he’s faced at least five times.

And he had virtually no issues on Tuesday — except for a lack of run support.

“He set the tone,’’ Aaron Boone said. “Early on, he didn’t have his best command. But he was still making pitches and there was good life on his fastball. He settled into a pretty good groove.”

Happ gave up a leadoff single to Ian Kinsler in the third and then walked Steve Pearce. With J.D. Martinez at the plate, both runners advanced on another Gary Sanchez passed ball.

Martinez then lofted a sacrifice fly to right to score Kinsler, as Pearce moved to third.

But Happ avoided further damage by getting Xander Bogaerts to fly out to shallow center, keeping Pearce at third before Eduardo Nunez also flied to center to keep the Yankees down by just one run.

Asked how he prevented the Red Sox from adding on, Happ said: “I just try to rely on experience and stay positive out there. That seems to work.”

Happ also pitched out of trouble in the sixth. Bogaerts reached on a one-out double and Nunez followed with a single to center, but Bogaerts stopped at third on the play and Happ got Brandon Phillips to pop to second and then fanned Brock Holt.

That strikeout ended Happ’s night after 102 pitches, trailing 1-0.

And although Happ ended up with another no-decision, the Yankees finally took advantage of his efforts when Neil Walker drilled a three-run homer in the bottom of the seventh following Chad Green’s scoreless top of the inning.

Much like Masahiro Tanaka, Happ has also been in top form in three straight starts.

He’s pitched six innings in each game and surrendered just a pair of runs — and only one has been earned. He is 6-0 with a 2.34 ERA in his last 10 starts. Most importantly, the Yankees have won each time.

For a team that needs each win to hold off the A’s in order to host the Oct. 3 wild-card game, Happ’s recent performance has been invaluable.