Bourjos supplied a two-run shot in the second inning to erase a 2-0 Dodgers lead.
Trumbo broke a 3-3 tie in the seventh with a single off Josh Lindbom (2-2), scoring Albert Pujols with the decisive run as the Angels took two of three from their interleague rivals.
Scott Downs (1-0) earned the win with a scoreless inning in relief of starter Garrett Richards, who had yielded three runs on nine hits over 6 2/3 frames.
Dodgers starter Aaron Harang went six innings, giving up three runs on eight hits.
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes