The Yankees didn’t sign Gerrit Cole to the richest contract in MLB history for a pitcher to be a grinder, but that’s what he was for most of Monday’s 9-3 win over the Rays in Game 1 of the ALDS.

When they needed him to pitch like an ace, though, the right-hander delivered.

“We were able to stop them when it really counted,” Cole said of his fifth-inning escape routine, when he left the bases loaded by fanning Manuel Margot to end the threat.

After the Yankees had given Cole a one-run lead — bailing Cole out following the two-run blast he’d allowed to Ji-Man Choi — the Rays loaded the bases with two out in the bottom of the fifth.

He walked Brandon Lowe, allowed a single to Randy Arozarena and then intentionally walked Choi after Cole fell behind 2-0.

But Cole recovered to strike out Margot with a 100 mph fastball to escape the jam.

“It was a big pitch in a big moment and it was executed perfectly,” Cole said. “I’m glad because I got myself into a bit of a mess there.”

He then tossed a scoreless sixth before Aaron Boone went to his bullpen — which performed well in a tight game before Giancarlo Stanton’s grand slam in the ninth blew it open.

So while Cole didn’t look the part of a $324 million pitcher in allowing three runs and striking out eight in six innings, he pitched like one just enough to give the Yankees offense enough time to get going.

In all, he allowed three runs over six innings, striking out eight, calling the outing “a grind.”

“I would agree with that,” catcher Kyle Higashioka said. “This is a tough lineup to navigate.”

“I thought he was good,’’ Boone said. “He was really grinding. He had to work hard a couple innings and made a couple huge pitches in the fifth and emptied the tank there and in the sixth. He made a lot of big pitches.”

And got plenty of support from a Yankees offense that is rolling and is making Cole and the rest of the Yankees’ pitching staff’s lives easier.

Boone hasn’t said whether he’d go back to Cole in a potential Game 5, but after Monday’s victory, they are a step closer to being able to save the right-hander for the ALCS.

“You want to be playing your best baseball when it’s most important,” Cole said.