CLEVELAND — The New York Yankees signed Gerrit Cole for games like this.

With the Yankees’ 99-win season on the brink, Cole spun seven sparkling innings, propelling New York to a 4-2 win over the upstart Cleveland Guardians on Sunday as the Bombers knotted the American League Division Series at two games apiece.

Starting for the 16th time in his postseason career, Cole gave the Yankees exactly what they needed, not just in staving off elimination but also in saving further wear and tear on a bullpen worn down by injuries.

“He just kept making pitches all night long,” Yankees manager Aaron Boone said. “I thought he was just really in command of the moment, and it was obviously a huge start for us and for him. And to get us that deep in the game set us up real nice.”

Cole allowed the Cleveland leadoff hitter to reach base in each of the first four innings, but every time it appeared he might be teetering on the edge of trouble, he was able to dial it up and escape with little to no damage on the scoreboard. He managed to pull off that trick while also keeping his pitch count under control so that he could work deep.

“For most of the night, in order to pitch around somebody, and overall, just stuff was pretty good,” Cole said. “But we just executed a lot of good pitches and mixed well. Well enough to get away with a couple of mistakes.”

One of those mistakes came in the fourth inning, when Guardians designated hitter Josh Naylor led off with a ringing line-drive homer to right center. As he circled the bases, Naylor went into an exaggerated celebratory gesture, rocking his arms back and forth.

If the intent was to put Cole off his game, it didn’t work — and couldn’t have worked, because Cole said he was unaware of Naylor’s antics until after the game.

“Whatever,” Cole said. “It’s cute. I didn’t see it in the moment, and it wouldn’t have bothered me in the moment. It just is kind of funny.”

Nothing could put Cole off his game in Game 4, as he held Cleveland to two runs over seven innings, struck out eight and, perhaps most important of all, threw 110 pitches.

The last of those pitches was a 98 mph fastball that struck out Guardians pinch hitter Will Brennan. As he stalked off the mound, Cole pumped his arms and screamed, the intensity on his face suggesting a person who knew he had done the job he was asked to do.

He had emptied the tank for his team.

“I do that every time I pitch,” Cole said.

The big blow for the Yankees’ offense was struck by emergent postseason hero Harrison Bader, who clubbed a two-run homer off Cleveland starter Cal Quantrill in the second to give New York an early 3-0 advantage.

Bader was acquired from the St. Louis Cardinals at the trade deadline while he was on the injured list with plantar fasciitis in his right foot. By the time he was able to work his way back and begin his Yankees career, the season was dwindling, and he played in just 14 games for New York during the regular season, hitting .217 with no homers.

He’s making up for lost time. Bader’s homer on Sunday was his third of the postseason. Bader, who grew up a Yankees fan, joined quite a list. In the storied history of the franchise, the only other Yankees center fielders to homer at least three times in a single postseason were Bernie Williams (three times) and Mickey Mantle (twice).

“I’m grateful and fortunate for the opportunity,” Bader said. “And every day I wake up, it feels good to be a Yankee. I carry that in the field, carry that in my preparation.”

With Cole reducing the workload of the New York bullpen to six batters, Boone was able to use closer Clay Holmes for three outs in the eighth and lefty Wandy Peralta to finish it off in the ninth. Both hurlers faced the segment of the Guardians’ order with which they best matched up, just as Boone would have scripted it.

“It lined up pretty well for us tonight,” Boone said. “You start looking back, it is like, man, every little out that sets up somebody in a little bit better position moving forward is always big.”

While Holmes’ availability or lack thereof has become a hot topic in the series, before Sunday’s game, Boone said that he could pitch in back-to-back games if he responds well to the first outing. Finding out whether that happened will surely be a topic during Boone’s pregame news conference Monday at Yankee Stadium ahead of Game 5.

Meanwhile, Peralta set down Cleveland in order in the ninth on just seven pitches. While the outing made it three appearances in three days for the veteran lefty, Boone said the efficiency of the outing made it possible that Peralta could be available for the series finale.

And because of Cole’s outing, the rest of the New York bullpen will be fully rested. Jameson Taillon will draw the Game 5 assignment for New York, going against Cleveland righty Aaron Civale.

“There is definitely going to be some added adrenaline and stuff when you step foot in Yankee Stadium,” Taillon said. “I will keep my day as normal as possible.”

While the Yankees’ beleaguered bullpen appears to be in good shape for the finale, so too will be Cleveland’s bullpen after manager Terry Francona avoided using any of his big three relievers — Emmanuel Clase, James Karinchak and Trevor Stephan — during the two games in Cleveland.

In other words, it’s going to be all hands on deck as the $68 million Guardians try to knock off the $246 million Yankees.

“If you would have told me back in March we just signed up to play Game 5 in New York, to go to the ALCS,” Francona said, “I would have jogged to New York. I mean, this is … I’m excited.”