Cabrera's solo shot -- his major league-leading 44th of the year -- put the Tigers up 2-0 and triggered a five-run outburst that iced the contest.
Jhonny Peralta also homered and Prince Fielder went 4-for-5 with a run scored, helping the Tigers win a second consecutive crown for the first time since claiming back-to-back AL championships in 1934-35.
Rick Porcello (10-12) allowed one run over five full innings to record the victory, yielding four hits and three walks while fanning three.
Jose Valverde wrapped up division-clinching triumph with his 35th save.
Cabrera's four hits gave him a batting average of .329 -- seven points better than Minnesota's Joe Mauer -- while his league-leading totals of 44 homers and 137 RBI put him on track for baseball's first triple crown since 1967 with two games remaining.
Royals starter Bruce Chen (11-14) was lit up for six runs (two earned) on 10 hits over 5 2/3 innings.
Alex Gordon homered for Kansas City.
Notable deaths of 2014 [PHOTOS]