Justin Morneau's sacrifice fly in the bottom of the third inning put Minnesota on top 1-0, but Cleveland scored three runs in the fourth, two on Shoppach's rally-capping homer. One of Dellucci's three hits capped the scoring with two outs in the fifth.
Asdrubal Cabrera added two hits for the Indians, who had lost seven of their previous 10 games.
Winner Paul Byrd (6-10) surrendered an earned run and six hits in seven innings. The 37-year-old right-hander has won his last three starts.
Denard Span and Delmon Young had two hits each for the Twins, whose two-game winning streak ended.
Losing pitcher Kevin Slowey (7-8) gave up five earned runs and six hits in six innings with no walks and seven strikeouts.
Celebrity Families of 2014 [PHOTOS]