If the Yankees’ offense is not going to pick up the slack that Aaron Judge can no longer carry, the club would be forced to play nearly perfect baseball in every other facet. 

So that’s what they did Saturday.

Luis Severino led the way, four relievers got the job done behind him and the Yankees shut out the powerful Rangers, 1-0, in front of a sellout crowd of 46,018 in The Bronx.

Jake Bauers’ arm took away one run, Billy McKinney’s bat provided the only run they needed, and the Yankees (42-35) won just their third game in their past nine.

Aaron Boone’s club will look to take the series behind Gerrit Cole on Sunday.

Since Judge hurt his toe June 3, the Yankees have played 17 games and scored 51 runs, just three per game and the fewest in baseball during that span.

The longer-term answer likely will entail getting an offense going that managed just four hits against Jon Gray and the Texas bullpen, but playing an otherwise flawless game works, too.

“I feel like that every day,” Boone said of the need to play sound, clean baseball. “Obviously it’s heightened when you’re playing low-scoring games. But I wouldn’t say it’s more of an emphasis now.”

Severino bounced back from a string of poor starts. He handed a one-run lead in the seventh inning to the Yankees’ bullpen, which closed it out with some drama.

Tommy Kahnle was excellent in the seventh.

Wandy Peralta got into two-on trouble in the eighth, but Clay Holmes entered and induced a ground out from Adolis Garcia and a strikeout of Josh Jung to escape danger.

In the ninth, Ron Marinaccio — the freshest arm they had — allowed a leadoff single to Jonah Heim and walked Mitch Garver.

But the righty bounced back to strike out Ezequiel Duran and Leody Taveras before Marcus Semien popped up.

“Whatever’s going on, he’s fearless,” Boone said of Marinaccio, who recorded the second save of his career and season.

Kahnle and Peralta were pitching for a third time in four games, while Holmes threw on back-to-back days.

The Yankees needed every out — and every play — they could get with such a narrow margin for error.

Their only run was scored in the fourth when McKinney smoked his fourth home run of the season. McKinney has reached base in all 15 games he has played this season, a rare find in a sea of offensive disappointments.

That was the only run the Yankees needed because Severino pulled himself out of a spiral — posting a 9.16 ERA in his prior four starts — with his best start of the year.

The Yankees righty was precisely what the club needed through six scoreless innings during which he allowed five hits and two walks.

He sported a fresh, throwback haircut, modeled after a season in which he finished third in AL Cy Young voting.

“I’m trying to get to 2017 Sevy, so I started with the haircut,” he said with a smile.

Severino was not always pinpoint, but he continually escaped — mostly narrowly with Bauers’ help in the first inning.

With runners on first and second base and two outs, Jung singled hard to right field, and the Rangers tested Bauers’ arm.

Bauers threw a strike home, on the fly to Kyle Higashioka, who tagged out Nathaniel Lowe for the final out of the inning. Bauers acknowledged he was rooting “a little bit” for the slow-footed Lowe to run.

“You always want to test the arm a little bit,” Bauers said.

That was the only hit in three tries the Rangers collected with runners in scoring position against Severino.

The Yankees’ pitching wasn’t perfect, but it was when it had to be — which is all the time without Judge.

“We have to go out there with what we got,” Severino said of the Judge-less Yankees, “and try to win games.”