Alex Rodriguez remained stuck on 599 career homers, but he drove in three runs to help the Yankees maintain a two-game lead over Tampa Bay in the American League East.
New York took three out of four from Cleveland, which has lost five of its last six.
The Yankees were protecting a 2-1 lead heading into the seventh, but they sent 12 men to the plate and scored all seven of their runs in the inning after two were out. Rodriguez and Curtis Granderson both had two-run singles during the frame.
New York drew three walks in the seventh and one batter was hit by a pitch.
Dustin Moseley (1-0) got his first victory of the year by holding the Indians to a run on four hits in six innings. It was his ninth win in a five-year career, most of it spent with the Los Angeles Angels.
Frank Herrmann (0-1) took the loss in relief. He gave up a single to Derek Jeter in the sixth that put the Yankees in front 2-1.
Cleveland scored three of its runs in the ninth off Chan Ho Park, who was left in to face all eight batters in the inning.
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