Sedin took a pass from behind the net from his brother Daniel and buried a shot behind Dallas goaltender Marty Turco. The Canucks, who had blown a two-goal lead, flew off the bench to congratulate Sedin. The exhausted Stars crawled off the ice.
Dallas outshot Vancouver 76-56 in the game, which started at 7:11 p.m. local time and didn't end until 12:35 a.m.
Many in the crowd sellout crowd of 18,630 had left before the longest game in Canuck history had ended. It also the sixth longest in NHL history.
The 76 shots given up by the Canucks was also a franchise record. That exceeded the 54 the New York Rangers managed against Vancouver in Game 1 of the 1994 Stanley Cup final.
The most shots by the Canucks in the playoffs was 47 against Toronto on May 24, 1994, against Toronto.
Dallas played 80 minutes, 48 seconds of overtime in a 4-3 loss to Anaheim on April 24, 2003. In that game the Stars had 63 shots on goal.
The longest overtime game in NHL history lasted 116:30 when Detroit beat the Montreal Maroons 1-0 back on March 24, 1936.
The Stars scored goals five minutes apart in the third period to force the overtime.
Antti Miettinen sparked the comeback by scoring at 8:31, and then assisted on Ladislav Nagy's tying goal at 13:46.
Nagy let go an innocent looking shot that went under the right pad of Canuck goaltender Robert Luongo, who was appearing in his first playoff game.
The Canucks looked like a beaten boxer barely hanging on by the end of the second overtime. Vancouver was outshot 11-3 and didn't get a puck on net until 13:48 of the period.
Vancouver was also forced to kill off 39 seconds of a two-man disadvantage when defenceman Kevin Bieksa and Lukas Krajicek were both called for high-sticking.
While the Canucks faded the Stars continued to move the puck with authority, crossing the Vancouver line in waves.
Luongo kept Vancouver in the game, flashing his glove to stop a Stu Barnes shot and got a pad on a Mattias Norstrom blast.
Vancouver's previous longest overtime game was a 5-4 win at Calgary on April 17, 2004. That overtime lasted 42 minutes, 28 seconds.
The Stars outshot Vancouver 16-3 in the third period and had a 40-22 advantage after regulation.
The Canucks looked to have the game wrapped up when Bryan Smolinski took a rebound off the back boards and gave Vancouver a 4-2 lead at 7:36 of the third.
Markus Naslund had a goal and an assist for Vancouver. Daniel Sedin and Mattias Ohlund, on the power play, also scored for the Canucks who missed last year's playoffs.
Brenden Morrow had a goal and an assist for Dallas. Trevor Daley had the other Stars goal.
Naslund broke a 2-2 tie at 13:47 of the second period when he fired a low, hard shot that beat Turco, who didn't look sharp on the play.
The Stars argued the Canucks had too many men on the ice but the goal stood.
Game 2 of the best-of-seven series will be played Friday (CBC, 9 p.m. ET).
The game wasn't the defensive chess match many had predicted. The teams played a fast, high-tempo match.
If Luongo was nervous in his first playoff game he didn't show it. He drew a line in the sand stopping Morrow on a 2-on-1 break when Dallas was shorthanded.
But he couldn't withstand the barrage when the game turned into a third-period shooting gallery.
Turco made some good saves, stopping Jan Bulis and Taylor Pyatt. He was serenaded by chants of "Turco, Turco" during the game.
Sedin opened the scoring at 4:20 of the first period when he banked a shot off defenceman Darryl Sydor's foot and into the net past Turco's outstretched glove.
Sydor made amends when he earned an assist on Morrow's goal at 5:28. Morrow unloaded a blast from the slot that got between Luongo and the post on the short side.
Ohlund made it 2-1 with just over six minutes gone with a bullet from the blue-line on a Canuck power play. Daley tied the score at the 10 minute mark on a long shot where Luongo was screened.
Defenceman Bieska, who missed the final game of the season with a foot injury, had a rough first period. He was called for three penalties and the Stars first goal came just 22 seconds after he was sent off for hooking.
The Canucks lost Matt Cooke with what seems to be a groin injury. Cooke didn't play in the third period. Alex Burrows was injured in the first overtime when he was crashed into the boards from behind on a hit by Mike Riberio.
Centre Ryan Kesler, out since January after hip surgery, was a surprise addition to the Canuck lineup.
Kesler had surgery Jan. 29 to repair a torn labrum, the cartilage that lines the socket of the hip. He missed the rest of the regular season but began skating with the Canucks this week.
He took a regular shift on a line with Burrows and Jeff Cowan.
The Canucks finished first in the Northwest Division - claiming the third seed in the Western Conference - and set a franchise record with 49 wins and 105 points.
The Stars had 107 points but were the sixth seed after finishing behind Anaheim and San Jose in the Pacific Division.
Notes-Defenceman Rory Fitzpatrick drew into the lineup after Brent Sopel was scratched with back spasms. ...Veteran Trevor Linden celebrated his 37th birthday Wednesday while Burrows turned 26. ...The Canucks had six players on their roster who played their first NHL playoff game. . ...Prior to the game there was a ceremony honouring the 1982 Canuck team that went to the Stanley Cup final.