The Angels jumped out to a 4-0 lead in the first four innings behind an RBI from Albert Pujols in the first, a two-run homer by Alberto Callaspo in the third and a Peter Bourjos sac fly in the fourth.
Down 5-1 in the eighth inning, the Twins scored two on a Joe Mauer single and a Ryan Doumit sac fly, but any chance of completing the comeback in the bottom of the ninth was dashed when the Angels put up a three-spot in the top half off Glen Perkins.
Jered Weaver improved to 5-0 on the season and now boasts a 1.60 ERA after going six shutout innings for the Angels.
The Twins and Angels will continue their three-game series on Tuesday at 8:10 p.m. ET.