Reddick had three hits for the A's, who had 13 hits and scored runs in six innings to extend their winning streak to six games.
Thursday was the 15th time this season Indians pitching allowed at least 10 runs.
With the scored tied 1-1, Oakland took control with a five-run fourth inning that was highlighted by a three-run double by Kottaras.
Reddick, who has 27 homers this year, hit a two-run home run in the fifth and singled in Coco Crisp in the sixth, putting Oakland up 10-3.
Oakland starter Jarrod Parker (9-7) allowed eight hits and five runs but still got the win. He walked three and struck out three.
Cleveland starter Justin Masterson (10-12) was lit up for eight runs -- all earned -- on eight hits over four-plus innings.
The Indians had 10 hits and five run-scoring rallies. Shin-Soo Choo had three RBI and Jason Kipnis had a home run -- his 13th of the season -- on a two-hit, two-RBI day.