Leon Draisaitl scored twice, Evan Bouchard had a goal and an assist, and Connor McDavid had two assists for the Oilers (21-12-3), who have lost two in a row for the first time since Nov 16-18. Pickard made 27 saves.
Edmonton lost 4-3 in overtime at the Los Angeles Kings on Saturday.
"Not our best," Draisaitl said of the loss Sunday. "I think we let off the gas a little bit after the first 10 to 13 minutes and gave them a chance to get back into it."
Draisaitl and McDavid combined on a power-play goal to extend their point streaks to 11 games and give the Oilers a 1-0 lead at 8:03 of the first period. McDavid fed Draisaitl in the right circle, and his one-timer went off Dostal's glove and across the goal line.
Bouchard made it 2-0 at 11:49, eight seconds after Edmonton killed a penalty. Viktor Arvidsson started a rush for the Oilers as he exited the penalty box, eventually passing the puck to Bouchard, who scored with a wrist shot from the top of the slot.
Gauthier cut it to 2-1 at 13:52. He brought the puck down the left side and scored with a wrist shot from the left circle.
"Just came off the bench so I was pretty fresh," Gauthier said. "I just started skating and I saw the defenseman came at me and just made a little move, and tried to get the shot off quick to surprise the goalie, and thankfully it went in."
Edmonton killed a double-minor high-sticking penalty on Troy Stecher that bridged the first and second periods.
McDavid and Draisaitl teamed up on another power-play goal to make it 3-1 at 9:10 of the second. McDavid fed Draisaitl out of the left corner for a one-timer at the right hash marks. It was Draisaitl’s NHL-leading 26th goal.