Verlander (12-8) surrendered one run on four hits, didn't issue a walk and struck out seven in the gem, hurling 75-of-112 pitches for strikes.
Kelly finished 3-for-4 for the American League Central-leading Tigers, who moved five games ahead of second-place Cleveland with their 14th victory in 15 games overall.
Justin Masterson (13-8) was touched for five runs on seven hits over seven innings for the Tribe, who dropped a second straight to their division rivals.
Ryan Raburn provided the Indians' only RBI.
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