Trumbo's two-bagger with the Angels clinging to a 3-2 lead in the seventh drove in Mike Trout (3-for-5, RBI), and Los Angeles went on to get RBI from Alberto Callaspo, Chris Iannetta and Aybar during a four-run uprising that put the game away.
Aybar drove in a run with a first-inning single for Los Angeles, which took the opener of a three-game series after Friday's scheduled game at Fenway Park was postponed by rain.
Tommy Hanson (3-2) earned the victory, yielding a pair of runs on seven hits over five innings.
Ernesto Frieri was called on to get the game's final out for his 14th save after Boston struck for three runs in ninth against Garrett Richards.
Red Sox starter Felix Doubront (4-3) was tagged for three runs on six hits over six frames.
Mike Carp went 3-for-5 with a solo homer and two RBI and Stephen Drew drove in two runs for the American League East-leading Red Sox.