CHICAGO — Had the Yankees given Jake Cousins some advanced notice that he might close out Tuesday’s win over the White Sox, he would have had plenty of time to sit and think about it.

Instead, the late notice may have helped him secure his first career save to help the Yankees in a pinch.

On a night when Clay Holmes was unavailable because he threw 45 pitches on Sunday and Tommy Kahnle got into early trouble in the ninth while attempting a four-out save, Aaron Boone called on Cousins to finish the job and the Illinois native was up to the task in a 4-1 win at Guaranteed Rate Field.

“I think [bullpen coach Mike Harkey] — he knows what he’s doing down there,” Cousins said. “Because the phone didn’t ring before he told me to get going. I’m pretty sure they told him ahead of time and he just knew first save, don’t let him sit with it. I appreciate that, because the adrenaline was definitely going.”

That was especially the case with Cousins having plenty of family and friends in attendance after growing up 45 minutes outside of the city in St. Charles, Ill.

“It was a ton of fun,” Cousins said. “Having a ton of family this [week], getting the first save here, like at home, in front of my family, is really special.”

Cousins, acquired from the White Sox on March 31 for cash considerations, has carved out a valuable role in the bullpen with his swing-and-miss stuff.

The Yankees needed it more than ever Tuesday night after Kahnle put runners on second and third to start the bottom of the ninth.

Once the inning started, Harkey told Cousins to start warming and soon enough, he was in the game.

Cousins struck out Korey Lee for the first out before walking Miguel Vargas on four pitches to load the bases.

But he did not buckle under pressure, getting a flyout and another strikeout to end it.

“Just a good job, being in that situation, not deviating from who he is and what he’s so good at,” Boone said. “Generated a lot of swing-and-miss with that slider again.”