NEW YORK — Maligned for poor defense and a bat that failed to fulfill promise for long stretches, Gary Sánchez impresses the Yankees with resilience.

With New York reeling after consecutive blowouts, Sánchez sparked a revival with an early go-ahead home run. Chad Green and Aroldis Chapman headlined four relievers who combined for 4 2/3 scoreless innings in a 4-3 victory over the Texas Rangers on Monday night that boosted the Yankees within a half-game of Toronto for the second AL wild card.

Sánchez put the Yankees ahead in the second against rookie A.J. Alexy (2-1) with his 22nd home run, and run-scoring singles by Aaron Judge and Gleyber Torres around Giancarlo Stanton's sacrifice fly built a 4-0 lead in the third.

Sloppy play behind the plate by Sánchez contributed to three defeats during New York's fall from a playoff position: He failed to tag a runner against the Mets despite catching the throw in plenty of time, allowed a pair of ninth-inning wild pitches at Baltimore and missed a foul popup in a seven-run inning by Cleveland.

"The first thing you learn," Sánchez said through translator Marlon Abreu, "nobody is going to be perfect playing this game. Even if you look at Gold Glovers, they're going to make some mistakes throughout the year. It's a tough sport, a long year. … The main focus is the next pitch. The next pitch is the most important one. You have to have that mindset."

Sánchez had 20 homers and 42 RBIs as a rookie in 2016, hit 33 homers with 90 RBIs the following year but has endured long slumps. He is hitting .211 with 52 RBIs this season, displaced by Kyle Higashioka as the catcher for ace Gerrit Cole.

"A guy that I feel has gotten beaten down and kind of abused over the years. It doesn't matter what it is," Judge said. "You see a lot of guys around the league and a lot of guys around the game that kind of get stuck in their ways and it's my way or the highway or this is just how I do it. But Gary is a guy that's always willing to listen, always willing to learn and continue to improve on his craft."

Yankees manager Aaron Boone expressed support for Sánchez before the game.

"Sometimes because Gary is the lightning rod that he seems to be sometimes, a play or two really torpedoes some of that or changes that narrative, and that's not necessarily fair," Boone said.

"I've just gained a lot of respect for the man," Boone added after the final out. "Even though he's had a tough week leading up to this, he does a good job of blocking things out and moving on even when he does make a mistake."

With a harvest moon rising above Yankee Stadium, New York built a 4-0 lead before the Rangers closed in a three-run fifth against Nestor Cortes. 

Green (8-7) retired five straight batters and Chapman three in a row for his 28th save in 32 chances — both pitching on four days' rest. Between them, Clay Holmes and Joely Rodríguez combined for the seventh and eighth.

After losing two of three to Cleveland (73-76), the Yankees (84-67) gained on Toronto and wild-card leader Boston (86-65) with 11 games left.

"If we play well, the results will take care of themselves," Boone said.

Charlie Culberson led off the fifth with a home run for Texas. Leody Taveras and  Isiah Kiner-Falefa hit consecutive doubles, Green threw a wild pitch that Sánchez hardly moved for, and rookie standout Adolis García hit a sacrifice fly.

Cortes escaped second-and-third, no-outs trouble in the first with three straight strikeouts and allowed three runs and five hits in 4 1/3 innings with seven strikeouts. 

Texas dropped to 55-95, on track for its first 100-loss season since 1973. Taveras airmailed a throw home from center field in the third, advancing the runners and leading to a run. 

"Those are little things that we shot ourself in the foot," manager Chris Woodward said. "We should have won that game. I hope everybody in that clubhouse realizes that."

Alexy, making his third big league start, allowed four runs, four hits and six walks in 3 1/3 innings. He's walked 15 in 18 innings.

"You can't stay in this league if you're going to walk guys like that," Woodward said.

OLD FRIENDS

Joey Gallo went 0 for 3 with a walk after missing 1 1/2 games with a sore neck, returning to play for the first time against the team that traded him to the Yankees in July.

"It's crazy. It's weird being on the other side," he said. "It brings a lot of emotion, a lot of memories."

TRAINER'S ROOM

Yankees: RHP Domingo Germán (right shoulder inflammation) could be activated as soon as Tuesday. Jameson Taillon (right ankle tendon) could throw in a minor league game Wednesday. 

LHP Jordan Montgomery (5-6, 3.63 ERA) starts Tuesday night against Texas RHP Dane Dunning (5-8, 4.28).