BOSTON — Maybe the Yankees are finally getting the J.A. Happ they were expecting.

And it could be just in time for October.

The left-hander delivered a second straight dominant performance in Saturday’s 5-1 win over the Red Sox on Saturday, limiting Boston to two hits and a walk in 6¹/₃ shutout innings.

It came after Happ limited the A’s to one hit over six innings in his previous outing in The Bronx and he hasn’t allowed a run in 15 ¹/₃ innings.

The turnaround has been stark for the 36-year-old, who had an ugly 5.57 ERA before his recent gems — and puts him firmly in the conversation for a playoff start.

“I don’t know how they’re gonna feel,’’ Happ said of the Yankees’ decision-makers. “If I feel like I felt today the next couple [starts], I like my chances. They’ll decide what they want to decide and whenever they ask me to pitch, I’ll pitch.”

Manager Aaron Boone said the final weeks of the season will help determine where players fit in the playoffs.

“I think that’s fair,’’ the manager said. “I think these three weeks are important to see where guys are at as we get into the decision-making process and how we’re gonna match up.’’

Happ said he hadn’t thought about his potential role: “That stuff always has a way of working itself out.’’

No doubt the Yankees have.

On Saturday, he gave up a leadoff single to Mookie Betts in the first. Betts was erased on an inning-ending double play from Rafael Devers and Happ retired nine in a row before Xander Bogaerts singled through the right side with one out in the fourth.

And the Yankees’ lineup, which was almost entirely shut down by seven Boston pitchers in Friday’s loss — when they managed just three hits — saw their first nine batters set down by opener Travis Lakins and Bobby Poyner on Saturday.

The Yankees didn’t get their first baserunner until DJ LeMahieu singled off Ryan Weber to open the fourth, which sparked a four-run inning, that was aided by J.D. Martinez losing Didi Gregorius’ double in the sun, which helped lead to a two-run double by Gary Sanchez and a two-run homer by Edwin Encarnacion.

“I feel like we came in with an edge and were irritated after [Friday] night,’’ Happ said. “They threw a lot of guys at us today.”

Happ pitched into the seventh, when Adam Ottavino entered and got the final two outs.

The Red Sox didn’t have a runner in scoring position until Tommy Kahnle gave up consecutive singles with one out in the eighth. Zack Britton got Brock Holt looking before Betts lined to right to end the inning. Aroldis Chapman allowed a two-out homer to Martinez in the ninth for Boston’s lone run.

But it was Happ’s 92-pitch performance that stood out.

“I’ve just felt a lot more like myself,’’ Happ said. “I wasn’t thinking as much and was able to throw strikes and settle in.”

If that continues, their playoff chances figure to improve.

Luis Severino seems to be nearing a return from his season-long absence because of rotator cuff inflammation and a strained lat. James Paxton is pitching well and Masahiro Tanaka is typically reliable in the postseason. Domingo German has already exceeded expectations this season and while the Yankees counted on Happ to be a key part of any playoff run they made this season, the lefty didn’t seem like he might be up to the task for much of the year.

That could be changing just in time.

Their next accomplishment could be knocking Boston out of the AL East race. Happ said the Yankees’ focus remained on their own team, but admitted: “They won the World Series last year and knocked us out [in the ALDS]. I’m sure it wouldn’t feel bad.”