With the Oilers trailing 2-0 late in the second period, Jordan Eberle fired in a goal with 4 seconds left in the frame to cut the Oilers' deficit.
Devan Dubnyk turned aside 27-of-29 shots and two more in the shootout for the Oilers, who are coming off a 2011-12 campaign in which they missed the playoffs for a sixth straight year.
Alexander Edler and Zack Kassian scored for the Canucks, who fell to 0-2-0 on the lockout-shortened season.
Luongo finished with 30 saves.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys