CLEVELAND — The Yankees hadn’t won an extra-inning game all season and Cody Bellinger stepped into the box as about half the hitter on the road that he is at home.

And he delivered to beat the odds that the Yankees are going to have to continue to overcome as a complete team — including one man short of an entire bullpen — while Aaron Judge is sidelined.

Bellinger’s tiebreaking one-out single in the 10th inning scored automatic runner Ali Sánchez and the runner that scared the Guardians into an intentional walk (Ben Rice) as the Yankees beat the Guardians 7-5 in a nearly four-hour Monday night marathon.

“It wasn’t pretty,” manager Aaron Boone said, “but very gritty.”

The Yankees improved to 1-3 in extra innings.

“We’re definitely going to have to win more games kind of like this, with a little bit more of a team effort,” Paul Goldschmidt said. “The guy [Judge] is probably the best hitter on the planet. He wins games for us by himself at times. We may have to do some things a little different like tonight — moving runners, stealing bases, stuff we’re already trying to do.”

Bellinger entered the game with a 1.140 OPS at Yankee Stadium and a .591 OPS on the road. Confounding splits that didn’t matter as he bested Shawn Armstrong’s 95 mph fastball with two strikes.

“I wanted to get the job done, keep it simple and not try to do too much,” Bellinger said.

The Yankees used their entire bench and all but one arm in the bullpen. David Bednar, the seventh reliever, recorded the final five outs — including three straight with the tying runs on base.

“It felt like a playoff game a little bit,” starting pitcher Will Warren said, “using that many guys.”

Goldschmidt, whose first-inning, two-run home run started the scoring, tied the score at 5-5 on an RBI fielder’s choice in the eighth inning. The Yankees had three singles in the rally but were robbed of taking the lead by one of the niftiest double plays of the season.

With the infield in, shortstop Brayan Rocchio slid to his knees, lifted his glove to snag a high bounce up the middle, tagged the base with the ball in his glove, rolled over and threw from one knee. The ball hopped but was scooped at first to get the speedy Jazz Chisholm Jr.

“It’s one thing to be there,” Boone said. “But he made a great play.”

At the same moment that lasers danced around the court at Madison Square Garden during the Knicks pregame introductions for Game 3 of the NBA Finals, fireworks went off high above center field 463 miles away in front of 29,517 fans at Progressive Field.

Entering with a runner on first and no outs in the sixth, Paul Blackburn was greeted by Angel Martínez’s go-ahead two-run home run to give the Guardians a 5-4 lead.

The Guardians erased a 3-0 deficit in the third inning with three runs on three hits, a wild pitch and a two-out run-scoring error by José Caballero, who couldn’t handle a short hop behind second base after the ball bounced through Warren’s legs.

Warren needed 91 pitches to get through 4 ¹/₃ innings, and the short outing prompted Boone to piece together the rest of the game.

“A lot of winning plays to get us to the finish line,” Boone said.

Ryan McMahon broke a 3-3 tie with an opposite-field home run that just cleared the 19-foot wall in left field to open the fifth. The ball was initially ruled in play as McMahon held up for a double but changed to a home run upon review.

As McMahon resumed his trot, an uproar came from the Yankees fans behind the first base dugout that the Guardians loyalists tried to drown out with boos. The battle of the fan bases continued every time a Yankees cheer erupted.

It was the second time in six days that the Yankees touched up Gavin Williams, a Cy Young candidate, for a pair of home runs. He won his previous start last Wednesday in The Bronx by limiting the damage to three runs over 5 ¹/₃ innings but didn’t reach the sixth in the rematch.

McMahon didn’t get another at-bat because Anthony Volpe (groundout) pinch hit for him in the seventh against slider-dominant left-hander Tim Herrin. As a result, Volpe — not McMahon — was up in the ninth with the go-ahead runner on first.

Cade Smith, the AL’s best reliever, struck out Volpe and stranded a leadoff single.

Two of the biggest outs by the parade of Yankees relievers came from left-handers Ryan Yarbrough and Tim Hill. All-Star right-handed slugger José Ramírez flied out to end the sixth and eighth innings, both times with two runners on.