Hunter's clutch smash against Rangers closer Joe Nathan (3-5) made a winner of Garrett Richards (4-3), who had recorded the final out in the eighth,
Mike Trout socked a solo homer for Los Angeles, which ended the contest two games behind the Oakland Athletics in the race for the final American League wild-card spot.
Kendrys Morales and Albert Pujols each provided an RBI for the Angels.
Nelson Cruz belted a two-run homer for Texas, which came into the game leading Oakland by 2 1/2 games in the AL West.
The Rangers were looking to clinch a playoff berth with a victory in the nightcap.