Trailing 5-4 entering the frame, Quintin Berry stole third with two outs and Delmon Young followed with a sacrifice fly, tying the contest.
Berry (3-for-5, two runs scored) added an RBI single in the eighth for an insurance run as the Tigers took the opener of a four-game series.
Octavio Dotel (3-2) was credited with the victory after tossing 1 1/3 frames of scoreless relief and Jose Valverde picked up his 17th save for Detroit, which won for the the eighth time in nine contests.
Torii Hunter went 4-for-5 with three RBI for Los Angeles.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys