Sam Colangelo, Ryan Strome and Alex Killorn also scored, while Jackson LaCombe and Cutter Gauthier each posted three assists for the first time in their young NHL careers.
Lukas Dostal earned his 18th win of the season with stops on 33-of-35 Oilers shots. The Ducks have now earned points in eight of Dostal's last nine appearances.
Edmonton's MVP duo of Connor McDavid and Leon Draisaitl each scored in the loss, which dropped the Oilers to 35-22-4 on the season. Calvin Pickard and Stuart Skinner combined for 20 saves.
Edmonton claimed an ultimately short-lived early lead with a power-play goal midway through the first period, a one-timer from McDavid to Draisaitl in the right faceoff circle.
Draisaitl's goal was the 392nd of his 11-year NHL career, tying Hockey Hall of Famer Mark Messier for the fourth-most in franchise history.
But the following 10 minutes would be all Ducks, as Anaheim took full control of the game with a sudden offensive explosion - chasing Pickard from the net and forcing Edmonton's star-studded attack to play from behind.
The tying tally came after a strong forechecking effort by Trevor Zegras and Alex Killorn, freeing space for Carlsson alone in the slot for a wrister by Pickard to the glove side.