ST. PETERSBURG, Fla. — The Yankees’ chances of making the playoffs all but disappeared over the weekend, the result of a four-game sweep at the hands of the Red Sox.

But there remain compelling reasons to watch, Gary Sanchez first among them.

Central is this question: Just what kind of numbers, in less than two months work, will he end 2016 with?

The rookie catcher, already with head-shaking numbers, added to them Tuesday night, crushing a tiebreaking three-run homer in the seventh inning to propel the Yankees to a 5-3 victory over the Rays in front of 12,732 at Tropicana Field.

With two on and two outs in the seventh, the 23-year-old Sanchez stepped in against Tampa righthander Brad Boxberger, who threw a first-pitch slider.

Sanchez, 0-for-2 with a walk to that point, pounced on the pitch and hammered it out to left-center for his 17th home run in a span of 136 at-bats (his first homer was Aug. 10) to give the Bombers a 5-2 lead.

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“There’s plenty of words,” said Mark Teixeira, who hit his 13th homer of the season in the fourth to cut the Yankees’ deficit to 2-1. “Amazing. Incredible. Impressive. He’s carried us. We’re not even close to talking about a playoff berth if Gary doesn’t come up and do what he does.”

The Yankees (78-72), who snapped a five-game losing streak, are 3 1⁄2 games behind Baltimore for the second AL wild card, but there are three teams (Detroit, Houston and Seattle) between them and the Orioles.

“I think it’s important that we put together some wins here and we put a streak together so we stay relevant,” Joe Girardi said before the game.

As Sanchez came to the plate against Boxberger, he said he expected to see a fastball.

But Sanchez said through his translator he had to adjust in a hurry.

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“It was not a fastball, it was a slider,” he said. “It was right there and I was able to put a good swing on it.”

First base was open and Rays manager Kevin Cash could have walked Sanchez to face Billy Butler, who already had two doubles in the game. Cash said afterward he felt walking Sanchez would lead to Girardi pinch hitting with Brian McCann.

Butler, who has seen Sanchez for only five games, smiled.

“He’s had a historic start to his career,” Butler said. “If they walked him, I would have been ready.”

He paused.

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“They’re probably going to walk him next time, I would think.”

Butler, 30, added later of Sanchez: “I’ve seen him hit every type of pitch out. I’ve seen him hit a cutter out, I’ve seen him hit a fastball out and I’ve seen him hit a fastball out. Basically if you leave it over the middle of the plate, it’s got a good chance of getting damaged.”

After Tyler Clippard allowed a run in the bottom of the eighth, Dellin Betances threw a perfect ninth for his 12th save.

Michael Pineda snapped his streak of three straight starts in which he didn’t make it out of the fifth inning, but only barely.

The righthander, who came in 6-11 with a 4.94 ERA, was mostly terrific but a high pitch count limited him to 5 1⁄3 innings. Pineda, working well with Sanchez, allowed two runs and five hits. With a solid changeup and wipeout slider, he struck out 11, one short of his season high, and walked one.

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Luis Severino (3-8) came next and threw 1 1⁄3 scoreless innings.

Drew Smyly allowed one run and four hits in six innings for the Rays (64-86), departing with a 2-1 lead, which his bullpen soon eviscerated, thanks to Sanchez.

“He’s meant a lot since he’s gotten here, both offensively and defensively,” Girardi said. “He can change games in a lot of different ways, so it’s kind of fitting he got the big hit again.”