Shields (10-8) allowed three hits and a walk, striking out nine while tossing 76-of-112 pitches for strikes.
The right-hander picked up his fourth victory in five starts as Kansas City avoided a three-game sweep.
Hosmer's RBI groundout in the first inning put the Royals ahead to stay and he added a two-run single to cap the scoring in the third.
J.A Happ (3-5) was reached for five runs (three earned) on six hits in a four-inning performance for Toronto.
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