Henrik Sedin scored one goal and assisted on Alexandre Burrows' goal. His brother Daniel assisted on both scores.
Burrows' first-period tally broke a scoreless tie, and Henrik Sedin scored off the rebound of his brother's shot on Oilers goalie Devan Dubnyk for a 2-0 lead midway through the second.
Roberto Luongo was barely tested by Edmonton, turning aside 11-of-12 shots and carrying a shutout until there were 5 seconds left in the contest, when Jordan Eberly scored on a power play.
The Canucks won their fourth straight road game and improved their record against Northwest Division foes to 8-1-1.
The Oilers, meanwhile, saw their stretch of six straight games with a point snapped.
Dubnyk took the hard-luck loss, stopping 30-of-32 shots.