The Athletics gave up the tying run in the bottom of the ninth but promptly scored in the first extra inning to avoid a sweep at the hands of the Angels.
Pennington tripled to open the 10th off Jordan Walden (0-1) and David DeJesus then grounded out to the pitcher. After Daric Barton was intentionally walked to set up the possibility of a double play, Jackson hit a chopper to shortstop that gave Pennington time to race home.
Brad Ziegler came on in the bottom half of the inning to retire the side on 10 pitches and earn his first save.
The win went to Brian Fuentes (1-2), who suffered a blown save in the ninth when he allowed an unearned run. Maicer Izturis reached on a fielding error by third baseman Kevin Kouzmanoff and pinch-runner Mark Trumbo eventually scored on a double by Bobby Abreu.
Barton's sacrifice fly in the third delivered the first Oakland run. That score was also unearned and spoiled an otherwise tremendous outing by Los Angeles starter Dan Haren, who gave up three hits and struck out five over seven innings.