Defenseman Eric Brewer had a goal and an assist during the final 20 minutes as the Oilers gained their seventh consecutive victory over the Mighty Ducks at Skyreach Centre.
After allowing three goals on just six shots in the third period, Anaheim goaltender Jean-Sebastien Giguere was penalized for interference with 3:32 remaining. Less than a minute later, Swanson cashed in with his first goal of the season.
Jussi Markkanen stopped all 15 shots he faced in relief of starter Tommy Salo, who yielded three goals on just five shots in the opening 11:32 of the contest to give Anaheim a 3-1 lead.
Petr Sykora netted two goals for the Ducks, whose last victory in Edmonton came on Feb. 15, 1999.