After two were out in the eighth, Alberto Callaspo singled, Maicer Izturis doubled and Peter Bourjos drew a walk from Greg Holland (4-3) to load the bases.
That brought up pinch-hitter Morales, who lined a pitch off the right field wall to drive in all three runners and hand the Angels a victory in the first of a three-game set.
Izturis finished 2-for-4 with an RBI for Los Angeles, which won for the third time in four games overall.
LA starter C.J. Wilson went 6 2/3 innings, allowing three runs on nine hits with one walk and six strikeouts.