Kipnes' run-scoring single in the sixth inning broke a 1-1 tie and Indians went on to clinch their three-game set series against the Athletics.
The Cleveland second baseman added a two-run triple in the eighth and scored on a wild pitch while Travis Hafner went 2-for-4 with an RBI for the Tribe.
Jeanmar Gomez (1-0), pitching while appealing a five-game suspension for hitting a batter in an April 14 game against the Royals, earned the victory with 5 1/3 solid innings. He yielded one run on four hits.
A's starter Brandon McCarthy (0-3) coughed up 10 hits over seven frames, allowing two runs while walking three and fanning four.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need