Donaldson, who was 3-for-5 in the game, came to the plate with the bases loaded and two outs and responded with a single into deep center field, bringing Jemile Weeks in from third with the winner.
Alberto Callaspo singled off Michael Kohn (1-3) to begin the ninth for Oakland, whose magic number in the AL West was whittled down to six games.
Grant Balfour (1-3) worked the top of the ninth and was credited with the win.
Mike Trout homered in the first inning for the Angels, who did not score again and were outhit 9-7 in the game.
Celebrity Families of 2014 [PHOTOS]