NEW YORK -- Normally a low-key person, Greg Bird turned to the dugout and let out a roar as he began trotting around the bases after his fly ball sailed into the right field seats Sunday night.

A sellout crowd at Yankee Stadium was ready to share those same emotions, but first, the fans needed to exhale when the final out was recorded.

Bird led off the bottom of the seventh inning with a homer, and Aroldis Chapman posted a five-out save as the New York Yankees staved off elimination Sunday night with a 1-0 victory over the Cleveland Indians in Game 3 of the American League Division Series.

Cleveland still holds a 2-1 lead in the best-of-five series. Game 4 is Monday night.

Bird hit his second homer of the postseason when he lifted a 1-1 fastball down the right field line. He briefly watched the ball soar halfway into the second deck, and when it was apparent it was going to be fair, Bird let out a yell while looking at the dugout. The first baseman then circled the bases.

"Yeah, I mean plain and simple, I'm not ready to be done playing, and I don't think the rest of the team is," Bird said. "So just very happy with that and knowing it gives us a chance."

He emphatically exchanged high-fives with his waiting teammates in the dugout. Aaron Judge removed Bird's helmet as the celebration continued.

"Just the way he's played in the playoffs and the way he finished up the year, I felt really good (for him)," Yankees manager Joe Girardi said of Bird, who was on the disabled list for more than three months due to a bruised right ankle before returning Aug. 26. "It's great to have him back healthy."

Bird's homer off Andrew Miller (0-1) helped the Yankees extend the series, but the win was not official until Chapman recorded the second-longest of his five postseason saves by striking out Jay Bruce and getting Carlos Santana to fly out with runners at first and second in the ninth.

Chapman entered the game after Masahiro Tanaka (1-0) allowed three hits in seven outstanding innings and David Robertson issued a one-out walk to Austin Jackson in the eighth. The left-hander was warming while Robertson pitched, and when Cleveland announced left-handed-hitting Lonnie Chisenhall as a pinch hitter, the Yankees went to their closer.

Chisenhall was replaced by right-handed-hitting Yan Gomes, who struck out on a 102 mph fastball. Chapman also fanned Giovanny Urshela with the same pitch to close the eight. He struck out Francisco Lindor with another fastball to open the ninth before Jason Kipnis and Jose Ramirez singled.

"He was great again," Girardi said of Chapman.

The Yankees recorded their first postseason shutout since a 1-0 win at Oakland in Game 3 of the 2001 ALDS. Before Bird homered and Chapman closed it out, Tanaka kept the Indians off-balance with his splitter while also getting help from his defense.

"It's multiple things," Cleveland manager Terry Francona said of Tanaka's split-finger delivery. "It's got so much movement to it, sinking down, and he's also got so much deception with it."

The Yankees turned a pair of double plays behind Tanaka in the second and fifth inning, but the biggest play occurred with one out in the sixth when Judge robbed Lindor of a two-run homer.

Lindor lifted a fly ball that appeared to have enough to go out, but Judge brought the ball back by extending his glove over the wall to make the catch.

"I wasn't making any contact (at the plate), so you got to make an impact in the game somehow," said Judge, who is 0-for-10 with eight strikeouts in the series.

Cleveland's Carlos Carrasco, who missed last year's postseason recovering from a hand injury, allowed three hits in 5 2/3 scoreless innings but exited after loading the bases in the sixth.

"I thought he was tremendous," Francona said.

NOTES: New York manager Joe Girardi heard significantly loud boos during pregame introductions. "I kind of expected it, you know," said Girardi, who acknowledged he erred by not challenging a hit-by-pitch ruling in Game 2. ... Cleveland RHP Trevor Bauer will start Game 4 on short rest, pitching against New York RHP Luis Severino. Bauer won Game 1 against the Yankees, tossing 6 2/3 scoreless innings Thursday. Severino lasted just one-third of an inning Tuesday in the AL wild-card game against the Minnesota Twins, surrendering three runs on four hits ... Indians DH Michael Brantley started for Edwin Encarnacion (sprained right ankle) and went 0-for-2 with a walk. ... Hall of Famer Reggie Jackson threw out the ceremonial first pitch.