New York Yankees first baseman Tyler Austin celebrates with Yankees...

New York Yankees first baseman Tyler Austin celebrates with Yankees catcher Austin Romine after he scores on his two-run home run against the Boston Red Sox during the seventh inning of an MLB baseball game at Yankee Stadium on Tuesday, Sept. 27, 2016. Credit: Kathleen Malone-Van Dyke

Three rookies the Yankees hope are cornerstones in 2017 and beyond kept the Red Sox from a Bronx celebration.

At least, Tuesday night.

With Gary Sanchez and Tyler Austin each hitting two-run homers and Luis Cessa turning in a solid six innings, the Yankees ended Boston’s 11-game winning streak with a 6-4 victory in front of 35,161 at the Stadium.

The victory kept the barely flickering playoff hopes of the Yankees (81-76) alive — though projections by FanGraphs had their chances at 0.0 percent entering the night — and kept Boston’s magic number at one for clinching the AL East.

The win wasn’t secured until Tyler Clippard, with two aboard, struck out David Ortiz — who else did you expect to be up? — with a full-count slider to end it, earning his second save.

“As players, we relish those moments,” said Clippard, who had allowed a combined four runs in his previous two outings, both in losses in Toronto. “I wouldn’t have had it any other way.”

Austin, whose playing time had dried up in recent weeks — he had only six at-bats during the recent 11-game trip — hit a tiebreaking homer off David Price in the seventh inning, his fourth, making it 6-4.

All of Austin’s homers have been go-ahead blasts, each to rightfield at the Stadium. The one against Price came on an 0-and-2 fastball.

“The 0-1 fastball, he blew it right by me, so I was just trying to stay short and hopefully he threw something similar to that again,” Austin said. “Luckily he did . . . he’s an unbelievable pitcher and I happened to put a good swing on the ball.”

The Red Sox (92-65), MLB’s leader in runs (865), had tied it at 4 with two runs in the seventh against Tommy Layne.

With Joe Girardi giving the recently ineffective Dellin Betances the night off, the manager had to piece together the late innings.

Righthander Blake Parker (1-0) and lefthander Richard Bleier got through the eighth, giving way to Clippard in the ninth. Clippard allowed a one-out double to Andrew Benintendi and a walk to Dustin Pedroia before getting Xander Bogaerts to pop to short and striking out Ortiz.

“Kind of the way fate had it,” Girardi said of Ortiz, the ultimate Yankee tormentor the last decade-plus, coming up in that spot.

Price (17-9, 4.04) was not sharp, allowing six runs and 12 hits, which tied a season high. The Yankees swatted three homers — one each from Sanchez, who hit his 20th, Didi Gregorius, who also hit No. 20, and Austin.

Cessa outpitched the Boston lefthander, allowing two runs, both coming in the sixth, and five hits in six innings. Coming out to the mound before the sixth, he said his back felt “a little tight” warming up, but he plowed ahead.

He allowed the two runs in the inning, but managed to get key strikeouts of Ortiz and Hanley Ramirez in the inning. Ramirez was 11-for-19 with four homers and 11 RBIs in his previous five games against the Yankees, but went 0-for-3 against Cessa.

“I feel more confidence in myself that I can pitch in the big moment,” Cessa said.

Few moments have seemed too big for Sanchez, who continues to bolster his AL Rookie of the Year credentials. His homer in the first gave him 20 in his 51st career game, tying him with Wally Berger (1930 Boston Braves) for fastest to 20.

“I’m a little surprised, but I worked very hard for it,” Sanchez said.

Girardi said Sanchez would get his vote.

“I can tell you Gary’s meant as much to this team,” Girardi said, “as any rookie in the big leagues this year. And he’s only been here a month and a half.”

More Yankees headlines


Unlimited Digital AccessOnly 25¢for 5 months