Rodriguez also hit an RBI single in the bottom of the first, when Matsui hit his 11th homer of the season. Rodriguez's major league-leading 30th homer came in the fourth.
Cano's sixth homer also was hit in the fourth. Miguel Cairo added a two-run double in the seventh.
Winner Chien-Ming Wang (9-4) yielded five hits in 6 1/3 scoreless innings.
Garret Anderson had two of the five hits for the Angels, who have split their last four games.
Losing pitcher Ervin Santana (5-10) surrendered nine earned runs and seven hits in three innings.
The Angels head into the All-Star break with four losses in their last six games.
Celebrity Families of 2014 [PHOTOS]