Joba Chamberlain (3-1) pitched a gem, throwing a career-high eight innings, giving up only two runs on only four hits, picking up his third win of the season.
The Yankees were able to draw first blood in the third when Nick Swisher grounded into a double play, scoring Derek Jeter.
Victor Martinez struck back in the fourth, driving a solo homer to right field, tying the game at one a piece.
After some good defensive innings, the seventh produced some offensive power. With the bases loaded, Swisher doubled to left field, scoring Pena and Gardner. Alex Rodriguez followed with a base hit off the glove of the diving shortstop, Asdrubal Cabrera. Mark Teixeira was picked off at second on the play.
That was plenty of support for Chamberlain. The Indians were able to add a run in the bottom of the seventh, but that was all.
Jeremy Sowers threw a strong five innings, giving up only one run on three hits. Aquino (1-1) picked up the loss in his ugly relief appearance. He pitched 1 1/3 innings, giving up only one hit but four runs due to his four walks. Luis Vizcaino and Jensen Lewis combined to finish the ball game for Cleveland.
Rivera pitched a perfect ninth, earning his eleventh save in twelve chances this season.
The Yankees lead in the AL East by one game over Boston. Cleveland remains in last place in the AL Central, now trailing by eight games with Detroit having the night off. Cleveland will look to rebound as they now have two series with division opponents coming up, starting with Minnesota tomorrow night.
The Yankees set a major league record playing their eighteenth errorless game in a row. The last error committed by a New York Yankee was back on May 13 when shortstop Ramiro Pena misplayed a ground ball in a game against Toronto.