Kipnis (3-for-4) ignited a six-run, first-inning outburst with a two-run double and Bourn (3-for-4, three RBI) capped it with a two-run single for the Indians, who drew five walks from Twins starter P.J. Walter in the big frame.
Corey Kluber (6-4) went 5 2/3 innings to notch the victory, allowing three runs on eight hits while walking one and striking out four.
Walter (2-3) managed to record only two outs, allowing six runs on just one hit.
Chris Parmelee went 3-for-5 with a pair of solo homers for the Twins.
Joe Mauer pounded a two-run shot and Oswaldo Arcia added a solo homer and finished with two RBI as Minnesota fell to Cleveland for a second straight game.