The Tigers tuned up for the playoffs, where they will open the division round this weekend in a series against Oakland.
Cabrera went 0-for-2, but became the first player in 45 years to win the triple crown -- leading the American League in batting average, RBI and home runs.
He batted .330, homered 44 times and drove in 139 runs. It is the 14th time that has been accomplished in one of the major leagues.
Cabrera was No. 1 in both leagues in homers and RBI. Only Buster Posey of the San Francisco Giants had a higher batting average, finishing at .336.
Carl Yastrzemski of the Boston Red Sox was the last triple crown winner, having done so in 1967 when he hit .326 with 44 home runs and 121 RBI.
Jackson's RBI double came in the fifth inning, giving the Tigers their 88th win of the season. They captured the AL Central for the second straight year.
Reliever Luis Marte (1-0) went 3 1/3 innings to get the win -- the second of his major league career. Luke Putkonen came on in the ninth to earn his first save in 12 major league appearances.
The winning run came off Luis Mendoza (9-10), who gave up six hits over seven innings.
Kansas City concluded its ninth straight losing season.