The second meeting of this three-game AL West series saw plenty of momentum swings, as LA scored four runs in the fourth to take a 6-3 lead, only to have the A's get two back in the seventh and put up four in their next at-bat.
David Freese's RBI single in the eighth brought the Angels within two runs at 9-7, and Sean Doolittle, who is trying to earn Oakland's closer's role from an ineffective Jim Johnson, couldn't hold the lead in the ninth.
Kole Calhoun, who went 3-for-6 with a two-run homer, opened the inning with a double, and Trout followed with his fifth home run of the season, one that landed in the rocks beyond the wall in left-center and set off the fireworks.
The celebration was premature, however, as Doolittle settled down to force extras and Johnson (2-2) pitched a perfect 10th prior to Oakland pushing across the game-winning run against Yoslan Herrera (0-1).
Jed Lowrie opened the 11th with his third hit of the night, and Donaldson chased him home with a double into the left-field corner to cap his own three- hit effort.
Johnson put the go-ahead run on second in the bottom half before grounding out Howie Kendrick to secure Oakland's fourth consecutive victory.
Trout opened the scoring with an RBI double in the bottom of the first and later scored on Kendrick's two-out base hit to center.
The A's answered with three runs in the third, as Eric Sogard and Lowrie each drove in a run sandwiched around John Jaso's RBI groundout.
Calhoun's two-out, two-run homer in the fourth capped a four-run inning for the Angels and ended Dan Straily's outing prematurely. The hosts pushed two across earlier in the frame when Chris Iannetta's RBI double was compounded by a Yoenis Cespedes error that allowed another run to score.
Sogard singled in a run and Craig Gentry scored on a wild pitch in the seventh, and Oakland retook the lead with four runs against Joe Smith in the eighth.
Brandon Moss evened things with an RBI base hit that ate up Albert Pujols at first, and after Cespedes worked a walk to load the bases, Alberto Callaspo singled to right to plate Donaldson with the go-ahead run.
Jose Alvarez relieved Smith and was greeted by a pinch-hit, two-run double back through the middle by Derek Norris.