Trailing 1-0 since the first inning, the Orioles put J.J. Hardy aboard in the seventh with a leadoff single off Indians starter Zach McAllister (4-2) and Thome lined a 1-0 pitch into the right-field seats, putting the Orioles ahead to stay.
It was the veteran slugger's 610th career homer, which moved him past Sammy Sosa and into seventh place on Major League Baseball's all-time list.
Ryan Flaherty added a solo shot in the eighth for Baltimore, which grabbed a 2-0 lead in their four-game series at Progressive Field.
Chris Tillman (2-1) collected the win, holding the Tribe to one run on six hits and a walk over 6 2/3 innings. He struck out four.
Troy Patton and Pedro Strop combined for 1 1/3 frames of scoreless relief and Jim Johnson racked up his MLB-best 29th save.
McAllister was saddled with the loss after yielding three runs on five hits over 7 2/3 innings. The right-hander didn't allow a walk and struck out six.
Shin-Soo Choo homered for Cleveland's only run.