Travis Moen scored at 2:07 of overtime to give Anaheim a 3-2 victory in a game the Canucks led 2-0 after two periods.
The Ducks lead the best-of-seven series 3-1. They can wrap up the series Thursday night in Anaheim.
"I didn't get a whole bunch on it," Moen said about his winning goal, that came off the rebound of a Scott Niedermayer shot. "The rebound popped out and I just kind of scooped it up and threw it at the net."
His shot beat Canuck goaltender Roberto Luongo over the right shoulder, silencing a sellout crowd of 18,630.
"I got pretty lucky it found it's way into the back of the net,"said Moen.
The Canucks looked like they had the game locked up when Brendan Morrison made it 2-0 at 17:31 of the second period.
With their backs to the wall, the Ducks refused to go down without a fight. They pressed Vancouver in the third period, making the Canucks scramble in their own end and turn over the puck.
Anaheim forced the overtime with third-period goals from Chris Pronger and Teemu Selanne. Sami Pahlsson had two assists.
"We had nothing to lose in the third," said Niedermayer, whose overtime shot bounced off Pahlsson. "It's not going to work every time but tonight it kind of went our way.
"We knew we had to attack and see what happened. It paid off."
The Canucks let a sure victory slip through their hands. They now can feel Anaheim's fingers around their neck.
"We were watching them, we stopped skating," said an angry and frustrated Morrison. "We stopped doing any of the things that helped us get the lead so we can look in the mirror at ourselves and question why we did that.
"We knew they were going to come hard (in the third period). We talked about it and then we went out and didn't adjust at all."
Some of the best Canuck players came up short. Henrik Sedin was on the ice for all three Duck goals. Taylor Pyatt was on for two.
Vancouver also took eight penalties.
"We used up a lot of energy with our defence, killing all those penalties that we took," Canuck coach Alain Vigneault said in measured tones.
"It's very disappointing, frustrating, use whichever word you want. We're up 2-0 (and) got a couple of chances to make it 3-0. We weren't able to do it and they kept chipping away."
Selanne tied the game with 5:42 left when he corralled the rebound of a Pronger point shot and beat Luongo.
Pronger scored the Ducks first goal with a seeing-eye shot through a forest of players at 3:58 of the third period.
"It takes 22 guys to believe you can come back," said Selanne. "That's what we did."
It looked like Morrison had iced the game when he scored late in the second period. His backhanded shot deflected off Moen and past goaltender Jean-Sebastien Giguere.
"It was nice to chip in and get that one back," said Moen.
Anaheim outshot Vancouver 30-26.
Luongo prevented the Ducks from winning in the third period when he stopped Selanne on a Anaheim power play, then got his glove on a loose puck just a whisker before Dustin Penner could reach it with his stick. In the second he got a leg on a Pahlsson attempt.
Markus Naslund had the other Canuck goal. Defenceman Mattias Ohlund had two assists.
The Ducks trailed after 40 minutes but had controlled much of the play. Anaheim spent a lot of the second period in the Canuck end but some strong work by the Vancouver defence resulted in few pucks getting to the net.
The shots that did get through were scooped up by Luongo, who has been nominated for the Hart Trophy as league MVP, the Lester B. Pearson Award as outstanding player in the eyes of his peers, and the Vezina Trophy as top goalie.
The Canucks dodged a bullet in the second period. Vancouver was already killing a penalty when Josh Green was given four minutes for high-sticking Teemu Selanne. Vancouver was able to kill off the 33 seconds of being two men short, then caught a break when Anaheim was called for too many men on a line change.
It was only the fourth game of the series but it had a Game 7 atmosphere. The crowd knew a loss meant it could be the final game of the season at GM Place.
Naslund opened the scoring at 12:55 of the first. Ohlund fired a shot from the point which Giguere blocked. With three Canucks crowding the net Naslund came up with the rebound and poked it home.
It was the third time in as many games Naslund had scored the Canucks' first goal.
Vancouver defenceman Kevin Bieksa, who missed the first three games, returned to the lineup. Taking a seat on the Canuck injury bandwagon was gritty forward Jeff Cowan, who the team said underwent "minor knee surgery." His place was taken by Nathan Smith.
Notes-The last Canuck to win an NHL award was Markus Naslund who won the Pearson in 2003. Pat Quinn was coach of the year in 1992. ....Other Canucks out with injuries are forwards Matt Cooke and Ryan Kesler plus defenceman Rory Fitzpatrick. ... Anaheim brothers Scott and Rob Niedermayer will appear on The Tonight Show with Jay Leno on Wednesday. ...canuck assistant GM Steve Tambellini is considered a candidate for the GM job in Phoenix.