The Angels were trailing 4-2 in the ninth when Erick Aybar collected a leadoff single against Athletics closer Grant Balfour. After Mike Trout flied out, Hamilton belted a pitch into the right-field seats for a two-run homer, forging a tie.
Then in the 11th, J.B. Shuck greeted Jesse Chavez (2-4) with a double, went to third when third baseman Josh Donaldson mishandled Aybar's sacrifice bunt and came home on Hamilton's fly to left.
J.C. Gutierrez (1-4) earned the decision and Ernest Frieri tossed a 1-2-3 bottom of the 11th for his 35th save as Los Angeles took the rubber match of a three-game series.
Trout hit a two-run homer former LA.
Coco Crisp and Yoenis Cespedes each hit a two-run homer for American League West-leading A's.