Sam Gagner also scored in the shootout for the Oilers, who were making their debut in the lockout-shortened season, while Devan Dubnyk stopped both Vancouver attempts.
The Canucks blew a 2-0 lead and have suffered back-to-back losses after losing 7-3 to Anaheim at home on Saturday night.
Jordan Eberle had the other goal in regulation for Edmonton.
Alex Edler and Zack Kassian scored for Vancouver.
Roberto Luongo, who was expected to be traded after being displaced as Vancouver's starter by Cory Schneider in last spring's playoffs, made his second straight appearance in the young season and finished with 30 saves.
Dubnyk finished with 27 to get the win.
Trailing 2-0 late in the second period, Eberle got the Oilers on the board by roofing a backhand past Luongo from a sharp angle with just four seconds left in the period.
Edmonton pressed for the tie in the third period, with Hemsky beating Luongo on a weak shot from the wing on the power play at 14:05.
The goal came after Andrew Ebbett took a penalty for tripping Oilers rookie Nail Yakupov, who was making his NHL debut.
Ryan Nugent-Hopkins had a chance to put the Oilers ahead with just over 2 1/2 minutes left in the third, but he fired wide on a rush. Luongo then stopped Eberle with 1:16 left, setting the stage for another shootout.
Luongo mopped up for Schneider in Saturday's loss to Anaheim.
[to top of second column]
Canucks coach Alain Vigneault to start Luongo against Edmonton in the second of back-to-back games rather than give Schneider a chance to redeem himself and restore some confidence.
"I had (the starting assignment) figured out a couple of days ago, and nothing that happened (Saturday) night changed my mind," Vigneault told reporters after the team's morning skate on Sunday.
The Oilers had 12 players in the AHL or in Europe during the lockout, while only four Canucks played overseas during the labor dispute.
Vancouver had trouble dealing with Edmonton's speed in the early going, but Edler opened the scoring at 10:58 of the first period, sending a slap shot by Dubynyk.
Play opened up in the second period, forcing Luongo to stop a Shawn Horcoff one-timer. A little while later, Kassian missed the net on two chances twice on the same shift before he doubled the Vancouver lead at 14:18.
NOTES: The Oilers have not qualified for the postseason since losing the 2006 Stanley Cup final to the Carolina Hurricanes. ... Justin Schultz, a highly coveted free agent signing who spurned other clubs, including the Canucks, played his first NHL game after beginning his career in the minors with Oklahoma City during the lockout. ... Vancouver defensemen Jim Vandermeer, Cam Barker and Andrew Alberts were scratched for the second straight game. ... Edmonton bench boss Ralph Krueger made his debut as an NHL head coach. ... Krueger scratched former Canuck winger Darcy Hordichuk, winger Magnus Paajarvi and defenseman Mark Fistric. ... The Canucks recorded their 410th consecutive sellout. .... Edmonton goaltender Nikolai Khabibulin is recovering from offseason hip injury.
Copyright 2013 The Associated
Press. All rights reserved. This material may not be published,
broadcast, rewritten or redistributed.