Haren (10-10) turned in a third straight start in which he has allowed two or fewer runs. The right-hander held the Athletics to a single tally on three hits and three walks.
Garrett Richards, Nick Maronde and Kevin Jepsen combined to hold Oakland scoreless for two frames as the Angels were clinging to a 3-1 lead.
Hunter broke the game open with a two-run single in the ninth.
Howie Kendrick added two RBI as Los Angeles pulled off its first three-game road sweep of the A's in nearly three years.
The A's said McCarthy never lost consciousness and was taken to Alta Bates Summit Medical Center in Oakland for observation.
Seth Smith drove in the only run for wild card-contending Oakland.
Celebrity Families of 2014 [PHOTOS]