BOSTON — Most September meetings between the Yankees and Red Sox come with October implications.

Perhaps the biggest stakes during their four-game set this week? Not finishing in last place of the AL East.

The Yankees still resided in the basement of the division as of Tuesday afternoon, but they pulled a little closer to the Red Sox by beating them 3-2 in the first game of a split doubleheader at Fenway Park.

After racking up 10 strikeouts and just one hit through five scoreless innings against right-hander Nick Pivetta, the Yankees rallied for three runs in the sixth inning to climb back to .500 (72-72).

In the process, they pulled within one game of the Red Sox (73-71) with 18 games left in a lost season.

The Yankees, who were officially eliminated from the AL East race on Monday night a year after winning it, have not finished in last place of their division since 1990.

“The end of the season is about having the discipline to go out there and still be at your sharpest and put your best foot forward,” Kyle Higashioka said after going 3-for-4 with a run in only his second start of the month. “At this point, we gotta show some character and finish strong no matter what the circumstances are.”

Adding to the lack of buzz in this series was the fact that the first game of Tuesday’s doubleheader was a makeup from Monday’s rainout, making it somewhat of a friends-and-family crowd.

Trailing 2-0 entering the sixth inning, the Yankees got on the scoreboard when DJ LeMahieu roped an RBI double to left field.

One out later, Gleyber Torres sprayed a single the other way to drive in two more runs for the 3-2 lead.

Randy Vasquez and Jhony Brito combined to toss six innings before handing it over to the only three healthy, high-leverage relievers the Yankees have left in Tommy Kahnle, Wandy Peralta and Clay Holmes.

Holmes nearly blew it in the bottom of the ninth when he lost the strike zone and walked the bases loaded on 16 pitches with one out.

But he got a gift when Alex Verdugo swung at the first pitch and grounded into a double play — with a strong turn from Torres and Anthony Volpe — to end it.

“That’s the one thing about Clay: even when he struggles a little bit with command and loses a couple guys, he’s always one pitch away,” manager Aaron Boone said before the nightcap.

Vasquez cruised into the fourth inning, when he gave up a solo homer to Rafael Devers and then a double to Triston Casas, who later scored on a wild pitch.

But across five spot starts this season, the 24-year-old Vasquez has now posted a 2.42 ERA as he tries to put himself in position for more starts next year.

“It’s an opportunity for me to gain the trust of the team and not just this year, but looking forward to next year,” Vasquez said through an interpreter. “Putting my name on the map and working and doing everything I can to get their trust.”

Brito later got out of a big spot with two outs and runners on the corners in the sixth inning, striking out highly regarded Red Sox rookie Ceddanne Rafaela in a nine-pitch battle.

While much of the Yankees and Red Sox’ focus at this point in the season has been about the future — they started a combined eight rookies in Game 1 (including Vasquez) with two more playing in Game 2 — there was also the veteran Higashioka delivering a three-hit effort despite being mostly pushed out of playing time by that youth.

“Higgy’s awesome,” Boone said. “He’s just a great teammate. Excited to see him get the walk-off [Sunday] and then have a day like he did today, not only offensively but behind the plate as well.”