Ramon Santiago and Victor Martinez also knocked in one run apiece in the eighth for the Tigers, who lead the White Sox by 5 1/2 games in the AL Central.
Detroit starter Rick Porcello gave up four runs on eight hits over seven innings, while Daniel Schlereth (2-1) tossed a scoreless eighth to pick up the win.
Jose Valverde worked around a two-out single and walk in the ninth to pick up his 40th save of the season. He is the second pitcher in Tigers history to register 40 saves in a single season. Todd Jones established a Tigers single- season record with 42 saves during the 2000 season.
Eric Hosmer hit a pair of solo home runs to record his first career multi- homer game for the Royals, who have lost two in a row since a two-game winning streak.
Nate Adcock made a spot start in place of Felipe Paulino, who was scratched earlier on Wednesday because of back spasms. Adcock allowed two runs on six hits over 5 1/3 innings.
Trailing 4-2, the Tigers scored three times in the eighth to take the lead. Blake Wood (5-2) started the inning on the mound and gave up a triple to Austin Jackson before Santiago’s sacrifice fly cut the gap to 4-3. Delmon Young followed with a single and scored on Martinez’s two-out double to left- center field. Martinez’s hit just got past a diving Alex Gordon. Alex Avila was intentionally walked to put men on first and second and Betemit followed with an RBI double off the wall in right. Avila also tried to score on the play, but was thrown out at the plate.
The Royals made things interesting in the ninth. With two outs, Valverde gave up a single to Chris Getz and walked pinch-hitter Brayan Pena. But Alcides Escobar flied out to end the game.
Detroit got on the board in the first. Jackson led off with a double, moved to third on a sacrifice bunt and scored on Young’s sac fly.
Hosmer led off the second with a solo homer to right to make it a 1-1 game.
The Tigers went back in front in the third. With runners on second and third and two outs, Adcock threw a wild pitch. Jackson, who singled earlier in the frame, scored on the play.
Hosmer’s second homer of the game in the fourth made it 2-2.
Kansas City then scored twice in the sixth to take the lead. Gordon led off with a single to center and scored on Melky Cabrera’s double to the left-field corner. Billy Butler followed with a single to left that Young misplayed, and the error allowed another run to cross the plate. Hosmer hit a bloop single to center, but Butler was tagged out at third and Porcello retired the next two batters to keep it a 4-2 game.
Detroit is 10-5 this season versus the Royals…Jackson went 4-for-4 with three runs scored…Royals outfielder Jeff Francoeur went 1-for-4 and is one hit shy of 1,000 for his career.