The Ducks will face the Oilers again in Edmonton on Monday.
Taylor Hall scored for the Oilers (17-20-7), who have lost seven of their past eight games.
The Ducks evened it up with just 1.1 seconds remaining in the opening period as Oilers center Jerred Smithson broke his stick on the faceoff and Fowler was able to pick up a rebound and bank in his first of the year season off Edmonton goalie Devan Dubnyk's pads.
Anaheim took a 2-1 lead with just under a minute to play in the second period as Palmieri tried to get a pass through to Teemu Selanne on a 2-on-1, but the pass was blocked by a diving Ladislav Smid. However, Palmieri was able to dig the puck from under Smid and deposit his 10th of the season behind Dubnyk.
The Ducks went up 3-1 midway through the third when Ryan Getzlaf made a great move to walk around Smid and then sent a backhand pass in front for Perry, who had an easy tap-in for the goal.
The Ducks hit the post twice with Dubnyk pulled for the final two minutes.
The Oilers announced Sunday that Ryan Nugent-Hopkins is out for the remainder of the season as he likely requires shoulder surgery.