Brantley's two-out double off Angels closer Fernando Rodney started the final surge for the last-place Indians, who have won three of five on a West Coast road trip.
After Rodney (4-2) hit Asdrubal Cabrera with a pitch, Choo extended his productive trip with the go-ahead hit.
Torii Hunter hit a tying homer in the sixth inning for the punchless Angels, who opened the three-game series with their 10th loss in 14 games.
Napoli hit two doubles for the Angels, who are essentially out of the race for their sixth AL West title in seven seasons. Los Angeles has rarely played meaningless September baseball in the past several years, but the Angels are 19-28 since hosting the All-Star game, managing just 21 runs in their last 10 games.
Cleveland's Carlos Carrasco again fell short of his first major league victory in his seventh start, although the longtime Philadelphia farmhand looked good in six innings of six-hit ball. Carrasco, acquired in last year's trade of Cliff Lee to the Phillies, yielded two walks and struck out six in his second start of the season.
Carrasco matched three-time All-Star Dan Haren, who gave up five hits over seven innings. Haren, who walked four and struck out six, has won just two of his nine starts since Los Angeles acquired him from Arizona in late July.
Haren struck out the side in the second inning and didn't allow a hit until the fourth, when Travis Hafner scored on Shelley Duncan's sacrifice fly.
Carrasco retired nine straight early on, but Los Angeles' Peter Bourjos drove a triple down the left-field line and scored on Alberto Callaspo's sharp single in the fifth. Haren then lost his control in the sixth, walking three straight to force in Cleveland's second run after Jayson Nix's two-out double.
Hunter swiftly answered with a shot to right field, his 20th homer of the season. After going 20 straight games without driving in a run, the Angels' clubhouse leader has knocked in four in the last three games.
NOTES: Hunter has hit 20 homers in nine of the last 10 seasons. ... Perez has allowed a run in just seven of his 57 appearances this season, keeping the opposition scoreless in 29 of his last 31 outings. ... In a quirky bit of scheduling, the Indians visited Angel Stadium for another three-game series way back in April, but the Angels won't visit Cleveland until next week.