Guthrie (3-0) earned his first win since April 9 with the strong performance, in which he scattered six hits and struck out five while working around three walks.
Jarrod Dyson chipped in with a pair of run-scoring hits as Kansas City took a second straight victory in their four-game home series.
Tribe starter Justin Masterson (4-2) was lit up for seven runs on nine hits in a 6 1/3-inning effort.
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