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 reside 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 (72-72) rallied for three runs in the sixth inning to climb back to .500.

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.

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, leading to 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 – one of which was Kyle Higashioka, who went 3-for-4 in only his second start this month –  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 made things dicey in the bottom of the ninth when he lost the strike zone, walking the bases loaded on 16 pitches with one out.

But he got a gift when Alex Verdugo swung at the first pitch of his at-bat and grounded into a double play to end it.

The Red Sox had taken a 1-0 lead in the fourth inning when Rafael Devers crushed a home run off Vasquez, his 30th of the season. 

One out later, Triston Casas doubled and eventually came in to score from third on a wild pitch.

Then, after the Yankees took the 3-2 lead in the top of the sixth, the Yankees threatened to rally back in the bottom of the inning.

They put runners on the corners with two outs before Brito struck out highly regarded Red Sox rookie Ceddanne Rafalea on a nine-pitch at-bat.