Corey Kluber outdueled Luis Severino as the Indians beat the Yankees 6-2 to open a three-game series in the Bronx.
Carlos Santana snapped a 2-all tie with a solo homer in the seventh inning to put Cleveland in front for good.
Jose Ramirez and hit a pair of homers and Austin Jackson also went deep for the Tribe.
Kluber allowed just three hits and two runs in eight innings to run his record to 13-and-4.
Severino slipped to 11-and-6 with the loss.
Chase Headley hit a solo homer and Todd Frazier singled in a run for New York in defeat.