Sanchez (4-6) scattered three hits, walked only one and struck out 10 in the dominating performance, in which he tossed 77 of his 105 pitches for strikes.
The right-hander retired the game's first 11 batters as well as the last 10 straight Royals hitters en route to his seventh career complete game.
Prince Fielder and Delmon Young each delivered an RBI single in the first inning to supply the offense for Detroit, which forged a first-place tie with the Chicago White Sox in the AL Central with the victory.
Kansas City's Bruce Chen (11-13) absorbed the hard-luck loss, allowing two runs on 10 hits in a 6 2/3-inning effort.
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