"I said: `This is pretty good, isn't it?' This is great," Boone said, recalling a quick dugout conversation with a coach. "This is what you live for, right? This is our best against the reigning MVP, a game on the line. Embrace that, love it. And our guys do."
Chapman struck Altuve on three straight 101 mph fastballs with two runners on base to end the game, and New York got a key hit from rookie Gleyber Torres during a three-run rally in the ninth inning to seesaw past the Houston Astros 6-5.
The Yankees won a wild one to take three of four from the team that beat them in Game 7 of the AL Championship Series last October.
"Winnable game, obviously frustrating because we were behind for so long in this entire series and we (still) could have split," manager A.J. Hinch said. "Split's not necessarily something to celebrate, but we should have won today."
Astros closer Ken Giles, who punched himself in the face after a rough outing earlier in this series, didn't pitch during New York's late comeback. Hinch was asked why he didn't use Giles, who hadn't allowed a run in eight outings before giving up four runs on Tuesday night.
"I thought (Will) Harris could get those guys out due to matchups," he said.
New York took a 3-0 lead into the seventh, trailed 5-3 going into the ninth and let a bounced third strike give the Astros their final chance.
"I had full confidence that Chapman would come through there and he really reached back for a little extra with Altuve -- probably the best fastball hitter in the league," Boone said. "Just a great job by Aroldis."
Altuve went down swinging, giving Chapman his seventh save and the Yankees a 6-1 record on their road trip against the top two teams in the AL West.
"Our whole road trip, going to Anaheim and getting three wins on a team that's one of the best in the game right now and then to come here in Houston and battle back after a tough first loss against them, that just kind of shows what kind of team we are," said Aaron Judge, who drove in the go-ahead run.
Houston, which had been shut out two days in a row, scored four times in the seventh and Carlos Correa added a solo homer in the eighth. The Yankees quickly loaded the bases with no outs in the ninth against Harris (1-2) on a walk and singles by Miguel Andujar and pinch hitter Aaron Hicks.
Brad Peacock came in and Torres, who finished with three RBI, hit a two-single to left that made it 5-all. With one out, Judge chopped a grounder that third baseman Alex Bregman charged -- instead of trying to get Hicks at the plate, Bregman threw to second, hoping to start an inning-ending double play.
Altuve caught the ball for the forceout, but dropped it as Torres slid in. Hicks scored on the play for a 6-5 lead.
Torres is hitting .317 with three doubles and five RBI in 12 games since being called up, a span where the Yankees have gone 11-1.
Chasen Shreve (1-0) got the last two outs of the eighth for the win.
Houston starter Lance McCullers yielded five hits and three runs in seven innings. He gave up all three runs in the first three innings and settled down after that, retiring 14 of the last 15 batters he faced.
The Astros trailed 3-0 and had managed just three singles when Yuli Gurriel and Josh Reddick hit consecutive singles with no outs in the seventh. Masahiro Tanaka hit Bregman with a pitch to load the bases, and reliever Chad Green was greeted by an RBI single from Marwin Gonzalez.
Brian McCann singled home another run and a passed ball by Sanchez tied it. Springer hit a grounder that was deflected by Green, and the go-ahead run scored.
Tanaka allowed five hits and three runs in five-plus innings.
Yankees: 1B Greg Bird (right ankle surgery) is scheduled to get his first at-bats on Monday in an extended spring game, Boone said. Boone said they have not decided whether he'll start in Class A Tampa or Triple-A Scranton when he's ready for a rehabilitation assignment.
THEY SAID IT
Boone on the at-bat by the 21-year-old Torres in the ninth: "That's what I expect. Poise, he's got that in spades. He's beyond his years. He plays with a confidence, maturity, so I feel great about him in that spot."
Astros: RHP Gerrit Cole (2-1, 1.73 ERA) will start in the opener of a three-game series against Arizona on Friday. Cole set the American League record for strikeouts in the month of April with 61 by fanning 12 in his last start.
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