Curtis Valk lit the lamp twice, including a late third period goal to tie the game at three, while Dane Fox also tallied to pace the offence for the Canucks.
Austin Lotz kept the Canucks in the game, making 29 saves on the night, including 13 in the first period alone as the Canucks were outshot 14-2 in the opening frame and trailed 1-0.
After the Oilers went up 2-0 just 1:50 into the middle stanza, Fox got Vancouver on the board, banging home a Hunter Shinkaruk cross-crease pass. It took the Canucks just under four minutes to record their next shot on goal, but they made good on the attempt as Valk wired home a wrist shot from just inside the top of the circle that beat Oilers goaltender, Laurent Brossoit.
After the Oilers regained the lead in the third period, Valk gathered a rebound and found the back of the net with less than four minutes to go to force overtime, where Mitch Moroz netted his second of the game to win it for the Oilers.
Next up, the Canucks take on the Winnipeg Jets on Sunday at 2:00 p.m.