Crawford singled in a pair of runs in a four-run fourth inning and Clayton Mortensen (1-0) held the Tigers off long enough to pick up his first win when the game was called after a rain delay of 1 hour, 45 minutes.
The Tigers had the bases loaded with two out in the top of the sixth when play was stopped.
Franklin Morales recorded one out before the rains came down and was credited with a save.
Justin Verlander (11-7) took the loss for Detroit, which has dropped six of its last eight games. Verlander allowed four runs -- three earned -- on six hits over five innings.