With the Tigers leading 6-4 in the seventh, Miguel Cabrera reached base on an error by Kansas City third baseman Mike Moustakas and Young blasted the first pitch he saw from Nate Adcock into the bullpen.
The Tigers would need the four-run advantage when the Royals rallied for three runs in the ninth off Jose Valverde on Billy Butler's two-run single and Moustakas' sacrifice fly.
But the Tigers closer struck out Jeff Francoeur with a runner in scoring position to end the contest and allow Detroit to clinch its three-game series.
Doug Fister (2-6) broke a personal three-start losing streak, despite allowing four runs on eight hits and walking three in six frames. He recorded two strikeouts.
Kansas City's Bruce Chen (7-8) was the loser, yielding six runs on nine hits in just 3 1/3 innings.
Butler and Moustakas combined to go 5-for-9 with six RBI, while Alcides Escobar added three hits and scored three runs for the Royals.