Kipnis and Cabrera launched back-to-back shots in the first inning and Cabrera added another homer in the fifth for a 3-1 Cleveland lead.
One batter later, Reynolds connected for a 460-foot home run that landed far up into the left-field stands, his American League-leading 10th of the season.
Jason Giambi went 2-for-4 with a two-run single in the victory.
Ubaldo Jimenez (2-2) earned the decision, yielding two runs on four hits over 5 2/3 innings while walking three and striking out eight.
Athletics starter Jarrod Parker (1-5) was roughed up for four runs on seven hits over five full frames.
Yoenis Cespedes homered and drove in two runs for Oakland, which dropped the opener of a four-game series.
Texas principal bans speaking Spanish, stirs controversy
Man spent 15 hours in jail for plugging electric car into an outlet at a school