Shin-Soo Choo added four hits -- including a solo homer and two RBI singles -- and scored four times, while Asdrubal Cabrera chipped in with three hits and two RBI for the Tribe.
Shelley Duncan supplied a solo shot as the Indians grabbed a 2-1 lead in their four-game set with the Orioles.
Josh Tomlin (4-5) collected the win despite getting tagged for five runs on seven hits in a six-inning effort.
Dana Eveland (0-1) started for Baltimore and was roughed up for five runs on six hits through 3 2/3 innings.
Chris Davis went 2-for-4 with a three-run homer for the Indians.