The Tigers ended a three-game losing streak while limiting the Indians to three hits.
Galarraga (4-5) retired the first 14 men he faced before giving up a two-out double to Jayson Nix in the fifth. Ryan Perry and Phil Coke each worked a perfect inning of relief to finish off the shutout.
Will Rhymes reached on a bunt single in the opening inning and a run scored on the play when catcher Lou Marson threw wildly to first. Rhymes then scored on a single by Asdrubal Cabrera.
The Tigers added two runs in the second on RBI singles from Gerald Laird and Austin Jackson.
Justin Masterson (4-12) took the loss, giving up five runs on 11 hits in six innings. He has had only one victory since July 1.
2014: The Year in Music [PHOTOS]