The win gave Cleveland, which has won 10 of its last 11 games, a sweep of the four-game series against the A's.
Jason Kipnis hit a two-run home run in the first inning while Nick Swisher led off the third with his fifth homer of the season and Reynolds added a two-run shot in the fifth that put the Indians ahead 9-0.
It was Reynolds' 11th home run, which leads the American League this year. Cleveland pushed its AL-best home run team total to 49.
Scott Kazmir (2-1) took advantage of the support in collecting the win. He gave up five hits over six innings. The only run he allowed was a sixth-inning home run to Josh Donaldson.
Oakland added a run in the eighth when Eric Sogard singled in the game's final run.
Cleveland battered Oakland starter Bartolo Colon (3-2) for eight hits and six runs in four innings.
After the Kipnis homer in the first, the Indians added three runs in the second, capped by a Kipnis sacrifice fly. Jason Giambi singled in a run in the fifth ahead of the Reynolds home run.
Wisconsin business offering 'therapeutic cuddling' forced to close
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance