Short's second home run of the season -- a one-out shot to left-center off Josh Taylor (1-2) -- broke a 1-1 tie in the sixth. It was his first career pinch-hit homer and the Tigers' third pinch-hit home run of the year, most in the majors
Taylor allowed three runs on three hits in relief of Royals' starter Zack Greinke
Will Vest (1-0) got four outs for the victory and Alex Lange earned his ninth save.
Both starting pitchers breezed through the first three innings, striking out a combined seven batters with just two reaching base, then both labored through the fourth.
Detroit was hitless until Riley Greene's one-out solo homer in the fourth. Greene's 440-foot blast into the right-center-field fountains was his fifth home run of the season. He also doubled and scored ahead of Short's homer.
Greinke surrendered one run on four hits and a walk, striking out five over five innings.
Tigers starter Matthew Boyd allowed a run on three hits and two walks, striking out six in 4 2/3 innings
The Royals tied the game, 1-1, in the bottom half of the fourth on MJ Melendez's bases-loaded grounder
Kansas City added a seventh-inning tally on three singles, capped by Vinnie Pasquantino's two-out hit, cutting Detroit's lead to 4-2. Pasquantino had three of the Royals' nine hits
The Tigers added insurance runs on Jonathan Schoop's two-run double in the eighth for a 6-2 advantage before Melendez snapped an 0-for-16 slump with an RBI hit in the bottom half of the inning
Bobby Witt Jr. capped the scoring with a ninth-inning sacrifice fly.
Rain delayed the game 29 minutes at the start.
By winning the rubber game of the series, Detroit finished its road trip 3-3. The Tigers will begin a seven-game homestand on Thursday with the first of four games against the Chicago White Sox
Kansas City has lost nine of 12 games overall and fell to 7-19 at home. The Royals will continue their six-game homestand against the Washington Nationals on Friday
--Field Level Media