Vancouver Canucks Trevor Linden watches the puck slide past Dallas Stars goalie Marty Turco and into the net after redirecting the initial shot during the third period. (CP PHOTO/Richard Lam)
Henrik Sedin also had a goal and assist for the Canucks, who battled back from a 1-0, first-period deficit. Taylor Pyatt and Bryan Smolinski added empty-net goals for Vancouver, which advances to the second round of the playoffs for the first time since 2003.
Linden broke a 1-1 tie when he deflected a Mattias Ohlund shot from the point that trickled through Dallas goaltender Marty Turco's pads and into the net at 7:00 of the third period. That brought a roar from a towel-waving crowd of 18,630.
It was the 34th playoff goal of Linden's career, tying Pavel Bure's franchise record.
Joel Lundqvist scored for Dallas. The Stars had used back-to-back shutouts by Turco to storm back from a 3-1 deficit to force the deciding match.
The Canucks still needed goaltender Roberto Luongo to make some big saves down the stretch. He stopped Stu Barnes on his doorstep, bringing chants of "MVP, MVP" from the crowd.
Luongo also got lucky when Mike Modano rang a shot off the post with less than four minutes remaining. Modano looked skyward in frustration.
The Canucks outshot Dallas 31-20.
Vancouver now travel to Anaheim to face the Ducks in the Western Conference semifinal.
The Canucks were able to win their first Game 7 in three attempts because they finally were able to put some pucks past Turco and get some production out of a power play that entered the game scoreless in 23 chances.
The Stars badly outplayed Vancouver in the first period, beating them to pucks and breaking up passing plays. The Canucks were lucky to escape trailing by only 1-0.
In the second, the Canucks finally began to play with some desperation and took advantage of a string of Dallas penalties to outshoot the Stars 15-4.
Henrik Sedin tied the game at 15:12 when defenceman Jon Klemm, making his first appearance in the playoffs, was called for cross checking.
Daniel Sedin set up the play, sending a long, cross-ice pass to his twin brother. Henrik, left alone in front of the net, beat Turco.
The points were the first for the twins since the opening game of the series and the goal was Vancouver's first against Turco in 167 minutes and four seconds. It also was Vancouver first power-play goal in 27 man advantages.
Lundqvist opened the scoring at 16:32 of the first period. He took a pass from Jeff Halpern, then using defenceman Kevin Bieksa as a screen, fired a shot over Luongo's glove.
The Stars had trailed 3-1 in a series 12 times but never before fought back to force a Game 7.
The Canucks are now 5-4 in Game 7's while the Stars are 5-6.
Vancouver wanted to erase the memory of their 2003 collapse against the Minnesota Wild. The Canucks led the Western Conference semifinal 3-1 but couldn't put the Wild away and ended up losing the deciding game 4-2, even though they had a 2-0 lead at one point.
Dallas played the game without defenceman Sergei Zubov who suffered a "torso injury" Saturday night. Klemm, 37, took his place in the lineup. Klemm has two Stanley Cup rings from his six years in Colorado.
Notes-It was the fourth consecutive playoff series that has gone seven games for the Canucks. . . Linden played in his ninth Game 7. ...Since the NHL introduced the best-of-seven format 119 series have gone to seven games. Heading into Monday the home team had won 75 of the deciding games.