Yankees reliever A.J. Cole looks on during the 10th inning...

Yankees reliever A.J. Cole looks on during the 10th inning against the Athletics at Yankee Stadium on Saturday. Credit: Kathleen Malone-Van Dyke

Reliever A.J. Cole hadn’t pitched since April 28 when Yankees manager Aaron Boone called him in to start the 10th inning with the score tied at Yankee Stadium on Saturday afternoon.

How many of the 41,859 in attendance on a blustery day even knew the Yankees had a pitcher named A.J. Cole on the team? Did the Yankees even know they had a pitcher named A.J. Cole on the team?

Cole, who was acquired from the Nationals for cash on April 23, made his first Yankees appearance five days later, throwing two shutout innings at the end of an 11-1 win over the Angels in Anaheim.

And then he sat. And waited. And warmed up. And waited some more.

For 13 days, Boone did not call on the 6-5, 238-pound number 67. Then the Yankees used up all of their available relievers on Saturday, and in he came.

Cole walked the first two men he faced. Understandable. Forgivable. But he then struck out Oakland’s No. 3 and 4 hitters (Jed Lowrie and Khris Davis) and retired Matt Olson on a foul pop to third to keep the score tied at 6.

“He just stayed like this the whole time he was out there,” said Aaron Judge, who has holding his right hand out and level to indicate Cole’s even keel. “After the walks, no emotion. He just stayed the same. That’s just the type of player he is. That’s why we got him on our staff.”

Cole threw a scoreless 11th, too, with a pair of strikeouts. When Neil Walker singled home Gary Sanchez with two outs in the bottom of the inning, Cole and the Yankees had a walk-off 7-6 victory, capping a comeback from a 6-2 deficit.

“So impressive,” Walker said. “It’s not easy to come out there and be sharp late in the game. Oakland has a good offensive club, so what he did today was I think more impressive than a walk-off [hit].”

How did A.J. Cole become the 13th man on the Yankees’ staff? He wasn’t even the Cole the Yankees tried to get during the offseason. That was Gerrit, whom Brian Cashman tried to acquire before he was traded from the Pirates to the Astros. Gerrit Cole is 4-1 with a 1.43 ERA and 86 strikeouts in 56 2⁄3 innings with Houston.

A.J. Cole, 26, is a former fourth-round pick of the Nationals who went 5-8 with a 5.32 ERA in parts of four seasons with Washington. The Nationals designated him for assignment on April 20 to make room for former Mets righthander Carlos Torres.

Life as the last man on any pitching staff is tenuous at best. Cole is 1-0 with a 0.00 ERA, but Cashman is known for shuffling the end of his roster like a blackjack dealer in Las Vegas. Eventually the Yankees will have to make room for injured position players Brandon Drury, Greg Bird and Jacoby Ellsbury — well, maybe not Ellsbury, who seems to have fallen into a very deep hole in Tampa — but carrying 13 pitchers and using one of them every two weeks might not be a luxury the Yankees can afford forever.

Cole knows he is not guaranteed tomorrow, but Saturday’s effort may have at least jumped him up to 12th on the staff ahead of David Hale, another righthander you may not have known was on the Yankees.

Hale, 30, threw three innings on Friday in the Yankees’ 10-5 loss to the A’s, so he was unavailable on Saturday, as was David Robertson.

So when the 10th came along, Cole was the last man standing.

“That’s a tough spot we put him in,” Boone said. “He hasn’t been out there since Anaheim. To go out and walk the first two batters, it’s almost understandable. There just hasn’t been those spots for him. To be able to not flinch, stay poised, make pitches — went through a tough part of the lineup — to really battle out of trouble and then settled in and gave us a couple good innings. So great effort by him. Really proud of him.”

Cole’s motivation was easy to understand: To be part of something. Finally.

“This team’s unbelievable,” he said. “They never give up. I went out there and gave it everything I had because I know they’re doing the same. I didn’t want to let them down.”