CC Sabathia (7-4) was charged with six runs on eight hits and two walks in 6 2/3 frames for the Yankees, who had won six of seven overall entering the series, but have now dropped 10 of their last 14 at home.
"It's not how you wanted it to end tonight, it did and you've got to move on," Yankees manager Joe Girardi said.
Derek Jeter singled and scored a run in the loss and is now just 10 hits away from 3,000.
The loss capped a disappointing day for New York, as it learned hours before the start of the game that reliever Joba Chamberlain would likely be lost for the season with a complete tear of the medial collateral ligament in his right elbow.
"I have no pain," Chamberlain said. "You could ask me to do anything. Just as far as being here, sitting here, [there's nothing]. A lot of guys who have had it feel a pop or certain thing -- it's hard to open doors, it's hard to do certain things. Nothing bothers me. That's what is really surprising for me.
"You're going to have to cut my arm off to stop me from pitching. But on the other hand, you have to realize this is your career. At 25, I'm still fairly young."
Hoping to reverse the Yankees' recent fortunes tonight will be young right- hander Ivan Nova, who is 4-4 with a 4.50 ERA. Nova was charged with a loss last Friday in Anaheim, but pitched well, allowing just two earned runs in six innings.
"It's really encouraging," Girardi said following that outing. "We saw him use his changeup. We saw him use his sinker. We saw him throw more strikes tonight. He walked two guys in six innings. That's good."
This will be his first-ever appearance against the Indians, who enter this series after losing two of three to Minnesota and have dropped 11 of 15 overall to see their lead atop the AL Central dwindled to just one game over the Detroit Tigers.
"Most of these guys that are here went through even tougher times last year," Cleveland manager Manny Acta said. "I don't think their confidence has wavered at all. It's human nature. One guy wants to win the whole game by himself and does way too much in certain at-bats, and the next guy does the same thing. You just have to let the game come to you and just take what the pitcher gives you, and go from there."
Getting the call tonight for the Tribe will be right-hander Fausto Carmona, who has lost four straight starts. Carmona's latest setback came on Saturday against the Texas Rangers, as he surrendered four runs and seven hits in 6 1/3 innings.
Carmona is just 1-4 lifetime versus the Yankees with a 6.53 ERA in 10 games, seven of which have been starts.
The Yankees won six of their eight meetings with the Indians last year and have won 10 of the last 13 matchups in the series.