CHICAGO -- After a wild and eventful night at the United Center, the Chicago Blackhawks have pulled off the improbable.

They've drawn even after losing the first three games to the Vancouver Canucks, the team with the best record in the NHL this season.

Now, do the defending Stanley Cup champions have one more left?

Ben Smith scored at 15:30 of overtime Sunday night, giving Chicago a 4-3 victory and sending the spirited and physical opening-round series back to Vancouver for Game 7 on Tuesday night.

"Anything can happen in Vancouver," said Smith, a rookie who made his NHL debut in October. "I'm just trying to take a deep breath every once in a while. ... They've got some great players. It's nerve racking when they've got the puck. They really took it to us for a while."

The Canucks played what coach Alain Vigneault characterized as their best game of the series. They made a goalie switch, turning to Cory Schneider in place of Roberto Luongo, who was pulled in the two previous games when he gave up 10 goals on 40 shots.

They still couldn't win.

And Schneider couldn't finish. When Chicago's Michael Frolik tied it on a penalty shot in the third, Schneider was injured while trying to make the save and it was Luongo on in relief.

"I just lost my legs and I seized up and couldn't do anything after that," Schneider said.

Chicago is attempting to become the fourth team in NHL history to win a seven-game series after falling behind 3-0. Philadelphia did it last year against Boston in the Eastern Conference semifinals.

"We just kept pushing," Vigneault said. "We need to find a way to change the momentum. Obviously, changing the goaltender and changing a few things up front were a way to try to get some of that momentum back. I thought we could have put it away, but we didn't. We're down to one game and we're going to play real hard."

Smith followed Niklas Hjalmarsson's shot from point that bounced off Luongo.

"I was just trying to fight for body position," said Smith, who has three goals in the series.

"I got a piece of it with my [stick] knob and I'm not sure exactly what happened," Luongo said. "I think Smith just chipped it over me on the rebound."

Daniel Sedin, Alex Burrows and Kevin Bieksa scored for the Canucks. Bryan Bickell and Dave Bolland added goals for the Blackhawks.

Chicago goalie Corey Crawford made 32 saves, including 12 in overtime.

"They were throwing a lot on net," said Crawford, another rookie. "It was probably the biggest game of my career. A lot of fun to win."

Schneider was hurt trying to stop Frolik's goal at 2:31 of the final period and had to be helped off the ice after making 17 saves.

Luongo faced only two shots on goal over the remainder of the third period, including one in a final frantic rush by the Blackhawks. Even though Chicago had the Canucks scrambling, the Blackhawks couldn't set up or find the go-ahead score and the game eventually headed to overtime.

With the teams playing 4-on-4 to start the third period, the Canucks took the lead on Bieksa's rebound goal 58 seconds in. He followed the puck in after a hard wrist shot from the right circle by Mason Raymond went off Crawford.

About a minute and a half later, Frolik was awarded the penalty shot when Dan Hamhuis took him down on a breakaway. Frolik skated in, faked one way and went the other to beat Schneider, who was got twisted on the play.

"I didn't listen to the crowd," Frolik said. "I focused on myself, tried this move and hoped it worked."

After Luongo replaced Schneider, the Canucks dominated play and had a chance to take the lead again, but Christopher Higgins' attempt hit the post with just more than 5 minutes to go.

Chicago defenseman Chris Campoli nearly whiffed on a clearing pass and Burrows was right there to convert from the slot, giving the Canucks a 2-1 lead with just over a minute remaining in the opening period.

After being foiled by Schneider on a power play in which they had a two-man advantage for 1:43, the Blackhawks tied it when Kane picked up a clearing attempt by Schneider and fed Bolland in the slot.

Vigneault said after Chicago's 5-0 win in Game 5 that Luongo was still the guy, but that changed. Luongo has, at times, has struggled against the Blackhawks in the playoffs over the last three years. But in others he was brilliant, like his 32-save shutout in the opener.

Schneider was making his first playoff start and just his third ever postseason appearance -- he relieved Luongo in Games 4 and 5.

"Coming out of warmups, we were surprised. That was something we didn't know about," Chicago coach Joel Quenneville said. "We thought Luongo was playing."

The Canucks scored first. After Hjalmarsson failed to clear a puck, the Canucks kept it in the zone and Daniel Sedin took a pass off the boards from twin brother Henrik Sedin and wrapped it around the goal and past Crawford just more than 2 minutes into the game. It was Daniel Sedin's fifth goal of the series.

Bolland's crushing hit behind the net on Vancouver's Hamhuis forced a weak pass and Bickell picked it off and beat Schneider -- who seconds earlier had ventured out of the net to clear a loose puck. That tied it at 1.

Chicago's Brent Seabrook, out for two games following a hard shoulder-to-head hit from Raffi Torres in Game 3, returned to the Blackhawks' lineup and withstood a hard check from Victor Oreskovich in the opening period.

Moments after Burrows hit the post on a power-play attempt, Torres was called for goalie interference. Raymond was assessed a hooking penalty, giving the Blackhawks a 5-on-3 for 1:43. The Blackhawks called timeout during the power play, but Schneider responded, turning away five Chicago shots.