Three Oilers, including NHL leading scorer Connor McDavid and defenseman Tyson Barrie, led Edmonton offensively with three points apiece.
"It's a pretty high-powered offense," defenseman Cam Fowler said. "You have to make them play a little bit more in their own end a little bit more than we did. A little bit too much one and done for us that allowed them to get in on their transition game and they have a lot of guys with a lot of speed that can really make you pay."
McDavid, who recently eclipsed 100 points for the fifth time in his NHL career, extended his scoring streak to 13 games with a goal and two assists, his fifth straight multi-point effort against Anaheim. McDavid totalled eight points in three games vs. the Ducks this season.
Leon Draisaitl, Brett Kulak, Jesse Puljujarvi and Ryan Nugent-Hopkins also scored for Edmonton.
Also with a goal and two assists, Barrie recorded the 21st three-point game of his 10-season NHL career.
John Gibson made 39 saves in his 50th start of the year. Zach Aston-Reese scored Anaheim's lone goal, his first as a Duck.
The loss dropped Anaheim to 28-31-12 (68 points) with 11 games remaining on the regular-season schedule.
Edmonton controlled much of the first period, directing 16 shots at Gibson in the opening 20 minutes and taking a 3-0 lead back to the locker room.
The Oilers first went ahead on a point shot by Barrie that snuck through traffic in front of the net and past Gibson.
Edmonton added to the lead midway through the period when the club was awarded a power play after Kane swatted at Gibson's glove following a save and was subsequently swarmed by Ducks defenders. With the Ducks now shorthanded, the Oilers quickly worked the puck to McDavid in the right faceoff circle, where he beat Gibson with a wrist shot over the netminder's right leg pad.
Nugent-Hopkins scored the visitors' third of the opening period, snapping a wrist shot by Gibson from the circle after a lengthy shift by the Oilers in the Ducks defensive zone.
"I think it was a slow start for us," Aston-Reese said. "Just a lot of the details like losing stick battles, puck battles. I couldn't block a shot tonight. I could not find the shot lane. I think that was the case for a lot of us. We just started behind the eight ball and it took the wind out of our sails. We regrouped a little bit before the third instead of completely laying down. We tried to get some momentum and we were able to get just a little bit. It was a tough night."
Puljujarvi, the former fourth overall pick, buried an insurance marker early in the middle frame, outmuscling Max Comtois for a loose puck in the slot and lifting it over a sprawled Gibson to give Edmonton a commanding four-goal lead.
Anaheim got on the board in the third period when Aston-Reese followed up his own rebound and potted the second chance opportunity past Oilers goaltender Mike Smith for his first goal as a Duck.
