Wilson (1-0) yielded only one run despite three hits and four walks. He struck out five for the Angels, who improved to 2-2 on the young season.
After Torii Hunter and Bobby Abreu each drove in first-inning runs, Los Angeles broke it open in the seventh when Abreu walked, Alberto Callaspo scratched out an infield hit and Chris Iannetta drove them both in with a double.
Iannetta went to third on an out and then scored on a suicide-squeeze bunt laid down by Erick Aybar.
Nick Blackburn (0-1) absorbed the loss after surrendering five runs on five hits. He walked two and struck out three as Minnesota fell to 0-4 on the season in its home opener.
Josh Willingham homered to provide the only run for the Twins, who are off to their worse start since 1981.