CHICAGO -- The taxed bullpen was on Nestor Cortes’ mind as he walked to the mound for his first inning on Tuesday at Guaranteed Rate Field, recognizing that the Yankees desperately needed the left-hander to provide length.

• Soto's first 3-HR game has Yanks gawking: 'He's the greatest hitter in the game'

Cortes delivered, turning in seven scoreless innings in the Yanks’ 4-1 victory over the White Sox. Though it came against a last-place club, Cortes believes his sharp effort can represent a turning point for his up-and-down season.

“I felt like something clicked for me today,” Cortes said. “Hopefully, I can continue to do what I did today for the next outing.”

Supported by the first three-homer game of Juan Soto’s career, Cortes held Chicago to just three hits in a 104-pitch, nine-strikeout effort, retiring the first 11 batters before Andrew Benintendi’s fourth-inning single. He did not walk a batter, using his sweeper and changeup frequently to keep the White Sox guessing.

“I feel like he’s been close to that, even while he’s gone through some struggles,” manager Aaron Boone said. “The changeup was really good for him tonight; life to the heater, the cutter was getting to where he wanted it. He was efficient. That [White Sox] team put up 18, 19 hits on us yesterday.”

Cortes finished strong, setting down the last six batters. His effort provided much-needed respite for a weary relief crew hammered for 20 runs over the past three games (11 2/3 innings).

“I realized that we’d played a lot of games the last week or so, and a lot of doubleheaders,” Cortes said. “You just want to go as deep as possible every time.”

Those rough numbers looked too familiar for Cortes’ taste, considering he’d hardly been “nasty” over the past five starts. Coming into the White Sox assignment, Cortes had allowed 24 runs over his last 23 1/3 innings (9.26 ERA), including 19 extra-base hits.

“As bad as it’s seemed for me, I felt like it was one inning or one pitch or one at-bat that got me off,” Cortes said. “I wasn’t able to come through that fifth inning; I know I’ve thrown four innings a bunch of times. It’s been that one pitch or that one at-bat where I got the base hit or the bleeder, the hard hit or the homer that hasn’t allowed me to go more into games.”

Even with Cortes correcting course, Boone had to navigate the final six outs cautiously. Mark Leiter Jr. allowed a run-scoring single to Luis Robert Jr. in a bumpy eighth inning, and Tommy Kahnle permitted two hits to open the ninth, prompting the hurler to kick a garbage can in the dugout.

Summoned for his first career save, Jake Cousins sealed the victory in the ninth, pinning the bases loaded.

“It was a ton of fun. I grew up 45 minutes from here,” said Cousins, a product of Park Ridge, Ill. “I have a ton of family [coming to the games] this week. Getting the first save here at home in front of family is really special.”