Bumgarner (4-9) rebounded from a horrible previous start in which he gave up eight runs in the first inning with a dominating performance Sunday, holding the Indians to one run on six hits while surrendering one walk.
Jeremy Affeldt tossed two shutout innings to close out the win, handing the Giants their fifth straight victory over interleague opponents.
Chris Stewart drove in two runs with a second-inning double and Aubrey Huff added an RBI for San Francisco, which improved its lead over second-place Arizona in the National League West to 1 1/2 games.
Cleveland's Fausto Carmona (4-10) lost for the seventh time in eight starts, surrendering three runs on seven hits through six innings.
Celebrity Families of 2014 [PHOTOS]