Hanson (2-1) put 10 men on base during the first five innings, but the Tigers could not come up with the clutch hit and wound up hitting into two double plays.
The Los Angeles starter gave up six hits and four walks and left the game holding only a 2-0 lead. The Angels then broke things open with a five-run eighth inning.
Los Angeles is tied for the fewest victories in the American League at five. Detroit has lost back-to-back games.
Peter Bourjos highlighted the big inning with a three-run triple and Bourjos then scored on a double by Trout.
Anibal Sanchez (2-1) took the loss, surrendering three runs on 11 hits in 6 2/3.
Four relievers followed Hanson to the mound and Dane De La Rosa eventually allowed Detroit's only run in the ninth on an RBI single from Miguel Cabrera.