CLEVELAND -- The New York Yankees and their closer Aroldis Chapman both worked overtime Saturday, but the result was a Yankee win, so it was worth it.

Brian McCann's two-out RBI double in the 11th inning drove in the deciding run, and Chapman pitched a career-high 2 1/3 innings to preserve a 7-6 victory over the Cleveland Indians at Progressive Field.

"We had to use our pen hard, but we've got time off coming up, so I was willing to do it," said Yankees manager Joe Girardi.

With two outs and nobody on base, Carlos Beltran singled and was replaced by pinch-runner Ronald Torreyes. McCann then doubled off the right field wall against reliever Tommy Hunter (2-2), scoring Torreyes with what became the winning run.

Chapman (3-0) came into the game to get the last out of the ninth inning and retired the side in order in the 10th.

"If it was still tied, I wasn't going to send him out for another inning," Girardi said.

But when the Yankees scored on McCann's hit, Girardi left Chapman in for the bottom of the 11th. Chapman gave up a leadoff walk to Jason Kipnis, but picked him off, retired Francisco Lindor on a fly ball and struck out Mike Napoli for the final out.

Asked after the game if he was tired, Chapman smiled and said, through an interpreter, "A little bit."

After New York scored three runs in the top of the sixth to take a 6-5 lead, the Indians rallied to tie it in the bottom of the seventh against reliever Dellin Betances.

Kipnis led off the inning with a double to right field. He went to third on a groundout by Lindor. Napoli walked, and Betances struck out Carlos Santana for the second out. But Jose Ramirez singled to right field, scoring Kipnis with the tying run.

Cleveland had a great opportunity to score in the bottom of the ninth. With Lindor on at second and Napoli at first, Santana hit a dribbler to the left side of the infield. Shortstop Didi Gregorius and third baseman Chase Headley converged on the ball, but Lindor ran into Headley, and was ruled out for interference.

Indians manager Terry Francona argued the call.

"My argument was that the guy (Lindor) ran into was not the guy fielding the ball, Gregorius was," Francona said. "(Lindor) was watching Gregorius, and ran into Headley. That was a big play because we would have had bases loaded and nobody out."

Miller struck out Ramirez and Chapman was summoned to relieve, and he struck out Juan Uribe to end the threat.

Cleveland scored a run in the first inning and both teams scored three runs in the third. Brett Gardner led off the Yankee third with a double against Cleveland starter Danny Salazar. Gardner went to second on a groundout by Jacoby Ellsbury. Gardner scored the tying run on a single to right by Beltran.

Salazar struck out McCann for the second out, but red-hot Gregorius hit an 0-2 pitch from Salazar into the seats in right field for his 11th home run of the season, giving New York a 3-1 lead.

It was Gregorius' fifth home run in the last 10 games.

"He's a talented player who is starting to figure things out," Girardi said.

Cleveland rallied for three runs in the bottom of the third on consecutive RBI hits by Napoli, Santana and Ramirez, giving Cleveland a 4-3 lead. Cleveland scored again in the fifth to make it 5-3.

The Yankees took control of the game in the sixth with a three-run rally that started with two outs and nobody on base. Salazar gave up singles to Chase Headley and Rob Refsnyder, putting runners at first and second.

Alex Rodriguez, who hadn't had an at-bat in the first two games of the series, pinch hit for Aaron Hicks. Rodriguez worked the count to 3-2 and drew a walk that loaded the bases.

Dan Otero relieved Salazar and Gardner poked a fly ball into the left-field corner that rattled around long enough to allow all three runners to score, with Gardner reaching third on a triple.

"Two-out runs break the other team's back, and our guys put up some tough at bats in that inning, Girardi said.

NOTES: Yankees RHP Chad Green was optioned to Triple-A Scranton/Wilkes-Barre. Green gave up three home runs in the first inning and four home runs overall in a 10-2 loss Friday. ... To replace Green on the roster the Yankees recalled RHP Nick Goody from Scranton/Wilkes-Barre. ... The Indians claimed LHP Tyler Olson on waivers from the Kansas City Royals and optioned him to Triple-A Columbus. ... LHP Tom Gorzelanny, who was designated for assignment by the Indians on July 4, declined his outright assignment to Columbus and elected free agency. ... Indians DH Carlos Santana has 20 home runs. He is the first Indians player to have 20 home runs prior to the All-Star break since Grady Sizemore had 23 in 2008. ... Indians 1B Mike Napoli has hit 13 home runs at Progressive Field this year. That ties Napoli with Baltimore's Mark Trumbo for the most home runs at home in the American League this season.