DETROIT — Their ace came up small, again, and they couldn’t hit, again, and still, the Yankees won.

They overcame another clunker from Gerrit Cole and an inability to produce with runners in scoring position thanks to a few mistakes by the Tigers and yet another brilliant performance from their bullpen in a 4-2 win at a frigid Comerica Park.

After Cole was knocked out in the second inning, five relievers combined to throw 7 ¹/₃ shutout innings, led by Clarke Schmidt’s 3 ¹/₃-inning outing.

“He was huge for us,’’ manager Aaron Boone said of Schmidt, who earned his first career win.

The Yankees scored in the first inning thanks to some hapless defense, as Detroit starter Tyler Alexander dropped a Josh Donaldson pop-up, and Aaron Hicks and Anthony Rizzo scored.

They added a run in the top of the second before Cole imploded in the bottom of the inning, issuing four of his five walks on the night.

Alexander lasted just one inning, with the left-hander struggling with his command. He needed 42 pitches to get through the frame, with a leadoff single by Hicks and walks to Rizzo and DJ LeMahieu that loaded the bases with two outs.

Donaldson then popped up, but catcher Tucker Barnhart couldn’t line it up, and the ball popped out of Alexander’s glove for a two-run error.

The Yankees added another run in the second, again thanks to some more Detroit pitching mishaps.

Isiah Kiner-Falefa walked, stole second and moved to third on a wild pitch that right-hander Rony Garcia bounced off the mound.

Garcia suffered a cracked fingernail that forced him from the game, and Detroit’s third pitcher of the night, Will Vest, gave up a sacrifice fly to Hicks to make it 3-0.

Then Cole lost his control in the bottom of the second, walking four batters — including Willi Castro to force in a run.

After the walk to Castro, Robbie Grossman hit a sacrifice fly to make it 3-2. Cole then walked Austin Meadows to load the bases again and end his awful night.

Schmidt entered and struck out Jonathan Schoop to end the inning. Schmidt went on to preserve the Yankees’ slim lead until Wandy Peralta entered to start the bottom of the sixth and pitched 1 ²/₃ shutout innings.

Meanwhile, the Yankees’ offense was quiet again, going 1-for-13 with runners in scoring position.

They stole a season-high four bases, two from Kiner-Falefa, one from Hicks and another from Rizzo.

Of the offense, Boone said, “Not a lot there. We had some chances, but couldn’t break through with a big hit. It was enough to shake hands at the end of the day.”

After getting the gift two runs in the first and the run in the third, the Yankees couldn’t generate anything against most of Detroit’s bullpen.

They managed to get two on and two out in the fourth, but Aaron Judge struck out. And with two on and two out again in the fifth, Joey Gallo struck out — his third of four strikeouts on the night as his ineptitude continues at the plate.

Clay Holmes replaced Peralta with one out in the seventh, walked Schoop, gave up a line single to Jeimer Candelario and with Miguel Cabrera at the plate, threw a wild pitch to send the runners to second and third.

Holmes fell behind Cabrera, 3-0, but got him to ground to third on a 3-1 pitch, and Donaldson threw Schoop out at the plate to keep the Yankees ahead. Holmes followed by fanning Spencer Torkelson to end the inning.

Miguel Castro tossed a scoreless eighth for the Yankees before LeMahieu came through with a bloop hit to right to knock in Hicks, for the Yankees’ first hit with a runner in scoring position.

Aroldis Chapman came in for the ninth and picked up the save.