NEW YORK -- The ball rocketed through the mist toward right field, and as Mark Teixeira tracked its flight, he spread his arms wide to embrace a memory that he will savor for the rest of his life. If this turns out to be his last trip around the bases, a walk-off grand slam to beat the Red Sox will do just fine.

Teixeira connected for his 409th home run in the bottom of the ninth inning on Wednesday, lifting the Yankees to a 5-3 victory that staved off playoff elimination at the last possible moment. Remarkably, the shot off Joe Kelly was Teixeira's first regular-season walk-off home run, joining a game-winning blast in Game 2 of the 2009 American League Division Series.

"I always seemed to hit those go-ahead homers on the road, but I never seemed to hit them at home," said Teixeira, who had the most homers without a regular-season walk-off entering Wednesday. "I'm like, 'Hey, if I finish my career and my only walk-off was in the playoffs, I'll take it.' I'll trade that for 10 walk-offs during the regular season. But this was a good one."

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The Yankees had been limited to one hit through eight innings and the scoreboard-watching Red Sox clinched the AL East title even before taking the field for the bottom of the ninth, by virtue of the Orioles' 3-2 victory over the Blue Jays in Toronto.

A Yankees loss would have eliminated New York from AL Wild Card contention, but they refused to buckle against Boston closer Craig Kimbrel. Brett Gardner singled and Kimbrel walked the next three hitters, forcing home a run. Kelly relieved and recorded two outs, but his second pitch to Teixeira was a 98.9-mph fastball that met loud wood.

"It's an unbelievable moment," Yankees manager Joe Girardi said. "Baltimore won tonight and you have to win or you're eliminated. To be able to come up with five runs in the ninth inning off of Kimbrel and Joe Kelly; Tex, he's had two big home runs in this last week. It's huge. It's a great moment for him and it's a great moment for us."

Statcast™ projected the ball's exit velocity at 107.1 mph, and though Teixeira knew he had hit it well, he wasn't about to flip his bat as he did earlier this week in Toronto -- not on a miserable night when strong winds had knocked down strong drives for both teams.

"That's a two-club wind for you golfers out there, a really bad wind," said Teixeira, who is retiring at the end of the season. "That's as good as I can hit a ball. I hit it really well and it still just got out. It just shows how windy it was."

While their postseason odds remain long, Teixeira said that it was a bonus that the slam spared the Yankees from seeing the Red Sox celebrate on their infield. The ball was delivered to Teixeira's locker, sticky with Gatorade but otherwise no worse for wear after its 419-foot journey.

"It meant a lot to him," Didi Gregorius said. "It's the end of his career and he's doing big things, especially here in front of the home fans. It's Tex being Tex right there."

Teixeira cradled the memento with pride, saying that he has kept about a dozen home run balls of significance during his career. Depending on the next four games, this one might be more meaningful than the rest.

"You don't want a wall-scraper in a 8-0 game to be your last one; you want a walk-off grand slam against the Red Sox," Teixeira said. "I'll still be trying to hit the next four games, but if it just happens to be my last one, that'll be pretty special."