Hunter put the Angels ahead with a first-inning RBI single and then lifted a two-run shot in the fourth for a 3-0 Los Angeles lead.
The Angels got the eventual game-winning run in the seventh when Chris Iannetta connected for a solo homer, and then survived a Twins' eighth-inning rally to post only their second win in eight contests.
C.J. Wilson (3-2) collected the victory, surrendering three runs on five hits over 7 1/3 innings while walking one and striking out four.
Scott Downs recorded the final out in the eighth after Minnesota had scored three runs, and then hurled a scoreless ninth to pick up his second save.
Twins starter Nick Blackburn (0-3) was touched for three runs on seven hits over six full innings.
Alexi Casilla went 3-for-4 with an RBI double for Minnesota, which fell for the eighth time in 10 games.
Celebrity Families of 2014 [PHOTOS]