TORONTO - Rookie Greg Bird rescued Andrew Miller. More significant on this night, Bird kept the Yankees' slim AL East hopes alive.

After Miller, 34-for-35 in save chances coming in, coughed up a one-run lead in the ninth, Bird's three-run homer in the 10th lifted the Yankees to a 6-4 victory over the Blue Jays in front of a stunned sellout crowd of 47,992 Tuesday night at Rogers Centre.

The Yankees (83-67), who received another standout outing by rookie righthander Luis Severino, pulled within 2½ games of the division-leading Blue Jays (86-65) with one game left in the three-game series.

"I think so,'' Joe Girardi said when asked if Bird's home run "saved'' the Yankees' division title hopes. "Mathematically, you're still in it, but with the way they've played and with us not having a chance to play them again, we would have dug ourselves a pretty deep hole.''

Toronto's Dioner Navarro sent a surge through the crowd in the ninth, homering with one out to tie it at 3. But Miller, after loading the bases with two outs, struck out AL MVP candidate Josh Donaldson to end the inning.

In the 10th, Toronto righthander Mark Lowe allowed a leadoff single to Brian McCann, who beat the shift with a bunt to the left side. Pinch hitter Slade Heathcott then reached on catcher's interference.

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Up stepped the 22-year-old Bird, who fell behind 0-and-2 before slamming a 2-and-2 slider into the visitors' bullpen in right-center. Of Bird's 10 homers, six have given the Yankees the lead.

"He's just so quiet at the plate, it's very impressive,'' general manager Brian Cashman said outside the clubhouse. "He literally has no panic to him. And so that serves him well in the highest-pressure environment.''

Bird, usually fairly reserved, ripped off his helmet and screamed upon re-entering the jubilant dugout, which Girardi said was "as energetic as I've seen it this year.''

Said Bird: "I was pretty pumped up. It's a big win for us.''

Of coming through in big situations, he said, "I'm just comfortable playing baseball. I don't really know how else to put it. But I enjoy it. I enjoy it here. Every day matters.''

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Miller, who allowed Edwin Encarnacion's 35th homer in the bottom of the 10th to make it 6-4, said of the Bird homer: "That saved me.''

Carlos Beltran had given the Yankees a 3-2 lead with a solo home run off Liam Hendriks with one out in the eighth.

Dellin Betances, making his 68th appearance of the season -- second-most on the team -- was called on to protect that lead, but had close to zero command. He allowed a hit and two walks, loading the bases with two outs, but struck out Encarnacion to end the threat.

Hendriks, who struck out Alex Rodriguez with the bases loaded to end the seventh, got McCann to pop out to start the eighth. But he grooved a 1-and-0, 97-mph fastball that Beltran blasted out to right for his 17th homer. Beltran also hit a sacrifice fly in a two-run first.

Severino was unable to hold that lead but still pitched well against the powerful Jays, allowing two runs and three hits in six innings.

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Toronto righthander Marco Estrada allowed two runs, both in the first inning, and six hits over 62/3 innings.

"It's huge,'' Beltran said of the victory. "If we're thinking about catching them, we have to be able to win against them. Today was a good game, tomorrow we have a chance to leave here winning the series.''