Guthrie (5-3) yielded five hits and three walks but was aided by a pair of double plays en route to the victory, which evened the Royals' season-ending three-game series.
Francisley Bueno and Kelvin Herrera each tossed a scoreless relief inning and Greg Holland fired a 1-2-3 ninth for his 16th save.
Doug Fister (10-10) surrendered three runs on seven hits over 4 1/3 innings for Detroit, which clinched the American League Central title Monday.
Triple-crown candidate Miguel Cabrera went 2-for-3 with a two-run single, improving his MLB-best batting average to .331 while raising his RBI total to 139, by far the most in baseball.
He entered the game with 44 homers, one more than Josh Hamilton of the Texas Rangers.
Senate Democrats to pull all-nighter on climate change
Dennis Rodman pledges to end trips to North Korea