Davis finished 4-for-5 with five RBI, two doubles and three runs scored, while Adam Rosales went 3-for-5 with an RBI and three runs scored for the Athletics, who snapped a four-game skid.
"It's just nice to get an opportunity to play," Davis said. "To get some hits and get them early, it takes a lot of pressure off yourself."
Ben Sheets (4-8) threw six shutout innings and gave up just two hits and a walk with four strikeouts for the win.
Cory Aldridge drove in the lone run, while Scott Kazmir (7-9) was blown up for a franchise-record 13 runs on 11 hits with three walks over five innings to drop his fourth straight start for the Angels, who have lost five of six.
"Between he's pitched some good baseball, and there's been some games that have gotten away from him," Angels manager Mike Scioscia said. "Tonight, obviously he struggled with a lot of things."
With the game scoreless in the bottom of the third, the A's used their biggest inning of the season to take a commanding lead.
Davis led off the inning with a double, stole third and came home on a wild pitch. Cliff Pennington then tripled and Coco Crisp blooped an RBI single to right. A single from Kevin Kouzmanoff was sandwiched by outs and Rosales kept the inning alive with an RBI single. Replays showed that Mike Napoli applied the tag to the back of Daric Barton, but home plate umpire Ted Barrett ruled Napoli missed the tag. Scioscia argued the call.
After Mark Ellis was intentionally walked, Ryan Sweeney walked to force home a run and Davis followed by blasting a 2-1 pitch over the left field wall for a grand slam and an 8-0 lead.
Oakland added five more runs to its lead in the fifth. Rosales led off with a single and went to second on a wild pitch. Davis doubled with two outs to score Rosales and, after Pennington singled, Crisp launched a 2-1 pitch over the wall in left. Barton followed by clubbing the first pitch he saw over the right field wall for a 13-0 lead.
Sheets had just one runner reach third base over his outing, in the first inning, and worked a 1-2-3 fifth and sixth inning before handing the ball to Jerry Blevins, who set Anaheim down in order in the seventh.
Aldridge's RBI triple in the eighth off of Ross Wolf got the Angels on the board.
Gabe Gross' two-run double in the eighth accounted for the final score.
Anaheim has won seven of the 12 games against Oakland this season...Sheets improved to 1-2 in five games against the Angels...Jered Weaver will take the mound for the Angels on Sunday and will be opposed by Trevor Cahill...The previous record for most runs allowed by an Angels pitcher was 11 by Scott Schoeneweis vs. Baltimore on May 23, 2001.