Soo Choo hit a fourth inning two-run single and Cabrera hit a two-run single in the seventh.
The winner was starter Jeremy Sowers (4-8).
Jensen Lewis, the last of five Cleveland pitchers, recorded his 11th save.
Detroit scored on Magglio Ordonez' first inning ground out and Curtis Granderson's two-run seventh inning homer.
Placido Polanco and Gary Sheffield both had two hits, while six others had one hit for the Tigers, who have dropped eight of nine.
Tigers Manager Jim Leyland was serving the second of a three-game suspension for inappropriate conduct on Sept. 15 and 16 against Texas.
Former Titans kicker dies in car crash
UPI Sports Results for September 20, 2014