Niedermayer's quick wrist shot from the left point came after his brother Rob levelled Vancouver's Jannik Hansen along the left boards. The puck squirted to Scott Niedermayer and he beat goalie Roberto Luongo low to the glove side on the Ducks' 63rd shot of the game.
"I was watching Brad May work in the corner for about 20 seconds, then the puck came out, my brother got a big hit on their guy and the puck slid to me," Scott Niedermayer said. "I just tried to get a wrist shot on net and I don't know if he didn't see it or what."
Luongo had kept the Canucks in it as they tried to stay alive in Game 5, and he finished with 56 saves.
"I think we felt good about how we were playing," Niedermayer added. "You will have nights like this where the puck is not going in, but keep doing it. I think he (Luongo) is what kept them in most of the night."
Jean-Sebastien Giguere had 26 saves for Anaheim.
The Ducks, who lost to Edmonton in the conference final last year, may have to wait for almost a week to find out their next opponent. Detroit and San Jose are tied 2-2 in the other Western Conference semifinal. If that series goes the distance, the seventh game would be played May 9.
Alex Burrows scored on a rebound past Jean-Sebastien Giguere to draw the Canucks even 1-1 with 8:57 left in regulation.
Samuel Pahlsson scored his first goal of this post-season 14 seconds into the second period when he jumped on a loose puck and poked it past Luongo, who was on his knees inside the net after being pushed back by Travis Moen's stick.
Luongo apparently had an equipment problem and wasn't ready to start the first overtime. Dany Sabourin filled in and the Ducks went after him, getting off five shots in the first 3:34 of the extra period.
When there finally was a stoppage, Luongo skated on and gave his backup a grateful pat on the head. Then he went back to work and made four saves during a Ducks power play that followed a delay-of-game penalty against Willie Mitchell midway through the first OT.
On Burrows' tying goal, Brandon Reid intercepted Joe DiPenta's clearing pass along the left boards and passed to Josh Green. Giguere stopped Green's slap shot, but Burrows was there for the rebound.
The overtime was the sixth for the Canucks in this year's playoffs, including winning in the fourth OT against Dallas in their first post-season game. Luongo made 72 saves in that 5-4 victory.
The Canucks had a two-man advantage for 1:32 after penalties to Corey Perry and Francois Beauchemin. But Giguere stopped all four shots Vancouver during the 5-on-3 power play, and Sami Salo's shot hit the post.
"We needed that win," Giguere said. "We didn't want to go back to Vancouver again.
"Roberto was playing so well tonight, he really gave them a chance. I thought we played the best game in the playoffs."
Luongo was under constant pressure through the first period, but vacuumed up everything the Ducks threw at him to keep it scoreless. Anaheim got off six shots in the opening couple of minutes, and finished the period with a 17-6 edge.
Among his 17 saves, Luongo was able to smother the puck on Sean O'Donnell's breakaway as time was running out in the opening period.
The 63 shots were a Ducks' playoff record.
Notes: The Ducks were eliminated 4-1 by Edmonton in last year's Western Conference final. After the season, Anaheim acquired D Chris Pronger from the Oilers. ... The Ducks made the Stanley Cup final in 2003, when the New Jersey Devils beat them in Game 7. ... Anaheim's penalty-killing unit has allowed only three goals in 56 short-handed situations during the post-season, and none in 33 at home.