The former Oilers goalie now has five shutouts in 16 games since joining the Wild and improved to 5-0 this season against Edmonton, split between Minnesota and the Arizona Coyotes.
Justin Fontaine had a pair of goals while Nino Niederreiter and Jordan Schroeder also scored for the Wild (30-21-7), who have re-entered the playoff race with a 10-1-1 record in their last 12 games.
The Oilers (17-33-10) have lost three of their last four.
The Wild started the scoring midway through the first period as Fontaine tipped a Christian Folin point shot past Oilers goalie Ben Scrivens.
Minnesota made it 2-0 with five minutes left in the opening frame as Niederreiter scored his 19th of the season on a big rebound from a Mikko Koivu shot.
The Wild went up by three goals with four minutes remaining in the second as Thomas Vanek made a great cross-ice pass to Schroeder, who put the puck in the net before Scrivens could get across.
Edmonton only had 10 shots on Dubnyk through 40 minutes.
The game's first man advantage went to the Oilers in the third period, but the Wild killed it, extending a perfect short-handed streak to 30 for 30 going back to Jan. 20.
The Wild made it 4-0 with just over a minute to play as Zack Parise fed the puck from behind the net to Fontaine, who scored his seventh goal of the season.
The Oilers remain home to face Anaheim on Saturday. The Wild return home to take on the Dallas Stars on Sunday.
Notes: Minnesota came into the game with a 9-0-1 record in their previous 10 visits to Edmonton… Out of the lineup with injuries for the Wild were Jason Zucker (clavicle), Matt Cooke (sports hernia), Ryan Carter (upper body), Keith Ballard (head) and Jared Spurgeon (concussion)… Absent for Edmonton were Tyler Pitlick (lacerated spleen), Taylor Hall (leg), Nikita Nikitin (shoulder), Viktor Fasth (knee), Anton Lander (shoulder) and Jeff Petry (ribs).