The Canucks snapped a two-game skid and, with 46 points, moved in front of Minnesota (44) for the top spot in the Northwest Division.
The four shutouts in a season marks a career high for Schneider, who made 23 saves.
Kevin Bieksa kicked off the Vancouver offense with a power-play goal late in the first period, Henrik Sedin scored his 10th of the season in the middle stanza and Chris Higgins scored along with Zack Kassian in the third.
Edmonton had a five-game winning streak and the loss dropped the Oilers out of the final playoff position in the Western Conference.
The battle for the last two post-season berths in the conference heated up with Detroit now holding down the seventh spot with 41 points and St. Louis in the eighth position with 40. Edmonton and Columbus both have 39 points while Nashville and Phoenix have 38.