"That's what it felt like, it was going to take a home run to get a run across," Ellsbury said. "Our bullpen pitched unbelievable to give us a chance to win that game. It was a nice team win."
The win took five hours and 32 minutes, going into the books after the Yankees absorbed a heavy dose of bad news, losing ace right-hander Masahiro Tanaka to the 15-day disabled list with inflammation in his right elbow.
Carlos Beltran also sustained two small facial fractures in a batting-cage mishap and Brett Gardner was held out of the lineup with an abdominal strain, but on the positive side, Mark Teixeira homered twice and Brandon McCarthy hurled 6 2/3 solid innings in his Yankees debut.
"No matter what happens before the game, in between the lines -- whether it's nine or 14 innings -- we're just going to keep playing hard," Teixeira said. "That's the only thing we can do. Don't feel sorry for ourselves, go out there and try to win games."
Ellsbury's homer off Vinnie Pestano made a winner of rookie Chase Whitley, who hurled two scoreless innings in his first outing since being bumped out of the rotation. David Robertson, the seventh Yankees reliever of the night, pitched a scoreless 14th inning for his 22nd save.
"That's a tough game to lose for either side," Yankees manager Joe Girardi said. "Both bullpens did an exceptional job. It came down to one big hit."
The Indians had the winning run 90 feet away in the 10th inning, as David Huff issued walks to three batters he faced, loading the bases with free passes to Michael Brantley, Carlos Santana and Lonnie Chisenhall.
Shawn Kelley entered and pitched out of the jam, striking out Nick Swisher and inducing a ground ball from David Murphy to wriggle free. New York's bullpen combined to hold Cleveland to three hits over 7 1/3 innings with nine strikeouts.
"Bases loaded, one out, any fly ball or solid contact gets the job done for them," Kelley said. "I was just trying to make a big pitch."
Teixeira atoned for a first-inning throwing error with his first multi-homer game in nearly two years, slugging a solo blast in the fourth and a two-run shot in the fifth, both off Tribe starter Josh Tomlin.
The second blast -- Teixeira's 17th of the season -- gave the Yankees their first lead of the night, marking his 37th multi-homer game and his first since July 13, 2012, against the Angels.
"I just got lucky. I just put a couple of good swings on some pitches," Teixeira said. "I haven't really been swinging the bat well the last few weeks, so it was just a good day to get two homers because we needed it."
McCarthy settled down after three unearned runs crossed the plate in the first inning, a frame prolonged when Teixeira hit Brantley with a throw as he slid into second base, loading the bases. Chisenhall knocked home a run with a groundout and Swisher delivered a two-run single.
Santana also logged a fifth-inning RBI single off McCarthy, who was acquired from the D-backs on Sunday in exchange for left-hander Vidal Nuno. He scattered nine hits with a walk and three strikeouts, recording 13 ground-ball outs to keep his infield busy.
"Results-wise it was all right, but I didn't feel sharp early on, I was struggling with a few things," McCarthy said. "I feel like I did a decent job of getting it back, but [catcher Brian] McCann was fantastic at keeping in touch with me between each inning, coming up, letting me know what he was seeing. We were able to make adjustments and it made it way easier for me."
McCann lifted a sacrifice fly as part of a three-run fifth inning off Tomlin, who worked seven innings and allowed four runs on eight hits. He walked none and struck out five before yielding to the bullpen.
"These ones are always tough when you lose them," Ellsbury said. "Obviously when you win them, it's nice for the momentum."