Lonnie Chisenhall hit a two-run home run for Cleveland, which had lost five of its previous six games.
Derek Lowe and two relievers gave the Indians a well-pitched game that was needed after their recent struggles. Cleveland gave up 35 runs to the Chicago White Sox last week while being swept in a three-game series.
Chisenhall's home run came in the second and the Indians added a run in the third on an RBI double by Michael Brantley.
After Chisenhall singled with one out in the fourth off Carl Pavano (2-5), Lou Marson walked and Shin-Soo Choo singled to load the bases. Kipnis hit the first pitch from Pavano over the wall in center for his ninth homer of the year.
Lowe (7-3) allowed a run on five hits over 6 2/3 innings.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff