Eddie Rosario had two hits and two RBIs and Jorge Polanco also had two hits for the Twins who evened the four-game series with the Indians at a game apiece — improving to 5-2 in the process. Cleveland sits at 5-3.
Dobnak (1-1) allowed just three singles and two walks while striking out four. Taylor Rogers pitched a 1-2-3 ninth to earn his second save.
Mike Clevinger (0-1) took the loss after allowing four runs on six hits and five walks in four innings. Clevinger, who struck out five, became the first Cleveland starter this season not to pitch at least six innings while also allowing two runs or fewer, snapping the franchise record at seven games.
Kepler gave Minnesota a 1-0 lead in the first with the eighth leadoff homer of his career and second of the season, driving a 3-1 fastball 444 feet into the upper deck in right-center.
Josh Donaldson followed with a single and moved to second one out later when Nelson Cruz walked. Rosario then lined a double into the gap in right-center that one-hopped the wall to drive in both Donaldson and Cruz.
Avila led off the second with his first home run of the season to make it 4-0, a 405-foot drive to right.
The Indians cut it to 4-1 in the sixth with a run off reliever Tyler Clippard. Jose Ramirez led off with a walk, stole second and advanced to third on a ground out by Francisco Lindor. He scored one out later when Franmil Reyes bounced a double up the middle past Polanco and second baseman Luis Arraez into shallow center.
Donaldson left the contest in the middle of the second inning with right calf tightness and is listed as day-to-day.