Corey Perry had a goal and assist in regulation and the only goal in a shootout, and Anaheim overcame a pair of two-goal deficits to beat the Canucks 6-5.
"I think it's a tribute to the guys recognizing around the room and on the ice and on the bench that we're not out of it just because we're down two," said rookie Bobby Ryan, who set up Anaheim's first goal and scored the next two.
Overlooked while sitting in 13th place on March 18, the Ducks have won eight of nine since then, moving into seventh in the Western Conference playoff race, one point ahead of St. Louis and two up on ninth-place Nashville.
"We feel like we belong in the upper echelon in this conference, and it's been a long year with a lot of inconsistency, and if we can manage to peak at the right time, then hopefully we can create some damage," Ryan said.
"We live another day," Ducks coach Randy Carlyle said. "It's the most important game of the season at this point. They all are at this time. When you're in a desperate situation as we are, there's no other way to explain it. Every point is precious and more precious as the games dwindle down."
The single point for getting the game to overtime was certainly valuable to the Canucks. It clinched a playoff spot, moved them into a tie with Calgary atop the Northwest Division and one point ahead of fifth-place Chicago in the race for home-ice advantage in the first round of the playoffs.
"We're in and now we're going to focus on seeing whether we can get home-ice advantage," Canucks coach Alain Vigneault said. "At the end of the day, that team right now with us is the second hottest team in the NHL and it went to a shootout. We battled hard and a point automatically clinches a playoff spot."
After a slow first 10 minutes, the teams seemed to score at will for the next 30, combining for 10 goals through the second period before failing to settle things through overtime. Anaheim blew an early two-goal lead before twice recovering from two goals down, setting the stage for Perry's heroics.
"Up, down, up, down, it's one of those nights where we just keep plugging away and we knew we were going to get our chances if we just kept going to the net and kept battling and we got rewarded for how hard we worked," Perry said.
Vancouver's top line of Burrows and identical twins Daniel and Henrik Sedin all scored. Kyle Wellwood and Ryan Kesler also scored for the Canucks, who returned from a 12-day, six-game trip to see their home winning streak end at 11 games.
The teams traded two goals each the final half of the first period.
Selanne, on a power-play deflection, and Ryan, on a long shot through Perry's screen, scored 3:16 apart midway through to give the Ducks a 2-0 lead.
Henrik Sedin pulled the Canucks within a goal with a shot through twin brother Daniel's screen two minutes later. After Ducks forward Drew Miller rang a shot off the post on a 2-on-1, Kyle Wellwood tied it with 1:15 left after a great play and pass by Steve Bernier, who was robbed earlier on a breakaway.
Vancouver failed to convert a lengthy 5-on-3 early in the second, but went ahead when Burrows banked a shot from below the goal line in off Hiller three minutes into the period for his 27th goal of the season.
Daniel Sedin added his 31st on a power play just over two minutes later.
Ryan, with a nice individual effort off the rush, and Kesler, on the tail end of a tic-tac-toe passing play, traded goals midway through the period.
Perry closed the gap only a minute after Kesler's goal, banging a rebound over Luongo after a sloppy Canucks line change created a 3-on-1 down low for the Ducks, and Selanne snapped a quick shot between the goaltender's legs off the rush to tie it with 3:32 left in the second period.
Hiller, making a third consecutive start ahead of Jean-Sebastien Giguere, made point-blank stops on Burrows' power-play shot in the final minute of regulation, and on Daniel Sedin's deflection with 50 seconds left in overtime.
"I don't mind five goals if we win," Hiller said. "We can definitely play better, more structure, but we'll take these two points and be happy about it."
Luongo stopped 27 shots through overtime.
- Ryan added an assist, giving him four goals and eight points during a four-game point streak, and increasing his lead among all NHL rookies in goals (28) and points (54).
- Henrik and Daniel Sedin both extended point streaks to six games, with 25 points combined over that time. Play was delayed after Daniel's second-period goal to clean up the mess left by a salmon thrown on the ice.
- The Canucks will play Saturday in Edmonton -- their eighth straight in a different city -- before returning home to face Colorado on Sunday.