After Baltimore scored two unearned runs in the second inning, Chris Davis, Travis Snider and Chris Parmelee homered in a six-run fourth that made it 8-0.
Cleveland got only two runners past second base all day in absorbing its first doubleheader sweep since Sept. 8, 2009, against Texas. Jason Kipnis, who started the day with a 20-game hitting streak, was a collective 0-for-7 with four strikeouts.
Manager Terry Francona was ejected in the ninth inning of the second game for arguing a third-strike call.
The Indians summoned Toru Murata (0-1) from the minors to make his major league debut in the nightcap.