The result: The Predators are heading back to Nashville with a split of the first two games in their Western Conference Semifinal series.
Suter tied the game with 1:07 left in regulation, Rinne made 18 saves after regulation and Halischuk scored the winner at 14:51 of the second overtime as the Predators evened the series with a 2-1 victory on Saturday night.
Halischuk, acquired from New Jersey last summer in a deal for Jason Arnott, took a perfect feed from Nick Spaling on a 3-on-2 rush and fired a high wrister from the right of the slot past Roberto Luongo's glove, ending the longest overtime game thus far in this year's playoffs – and the longest game in Nashville history.
"Smitty (Jerred Smithson) did a great job winning the draw and (Shea Weber) threw it over to Suts (Ryan Suter) there, he had great battle on the wall and made a great pass over," the 22-year-old said. "Smitty was driving the net and (I) kind of picked my spot -- luckily it went in."
Halischuk, whose biggest previous goal came in January 2008 when the Toronto native got the overtime winner in the gold medal game of the 2008 World Junior Championships, said it was tough to compare the two.
"It's hard to compare right now," he said. "Maybe I'll look back at it one day, but definitely I think this is the most exciting it's been so far for sure."
Nashville coach Barry Trotz said his third line did everything right on the winning goal.
"They put pressure on the puck, they turned it over at the blue line, and Hally placed it right where he needed to put it on Roberto," Trotz said.
Suter made the overtime possible by banking the puck into the net off goaltender Roberto Luongo for his first goal of the playoffs and Nashville's first of the series.
"I was just trying to get a whistle, I knew there wasn't much time left," Suter said. "I just wanted to get it on him and hopefully (Luongo) would've covered it. Then we could've drawn up a face-off play or something. I got a fortunate bounce there and it went in."
The series moves to Nashville for Games 3 and 4 on Tuesday and Thursday.
It was the 11th night in the last 12 that at least one playoff game has gone to overtime – the exception was Thursday, when Vancouver won the series-opener 1-0 in the only game of the night. In all, this was the 16th of the 54 playoff games this spring that has gone to OT.
Rinne, who faced only 15 shots through 60 minutes, was the reason that Halischuk had the chance to be the hero. He robbed Henrik Sedin 4:15 into the first overtime, then made the save of the playoffs with 2:15 left in the first extra period when he dove from left to right to deny Kevin Bieksa on a one-timer off a pass by Daniel Sedin that appeared headed for the back of the net.
"Obviously, I was a little bit fortunate," Rinne said. "Sedin made a nice pass to Bieksa and I was able to get my blocker and my stick over there."
A minute later, he got his left pad on Maxim Lapierre's shot from 10 feet after Lapierre dangled through the defense. He also denied Daniel Sedin on a rebound early in the second overtime.
"We had chances but were unable to beat a great goaltender," Vancouver coach Alain Vigneault said.
Unlike Game 1, when the Predators rarely tested Luongo, Nashville dominated much of the game, but trailed 1-0 on Burrows' shorthanded goal early in the second period until Suter finally found the back of the net to force OT.
With Rinne on the bench for an extra attacker, Suter followed his own blocked shot behind the goal line to the right of Luongo and shoveled the puck towards the net. His passout deflected off the inside of Luongo's left skate and into the net for first of the playoffs with 1:07 remaining.
"Tonight we played Predator hockey. I talked about the disappointment (after Game 1), but we played with conviction, we played with discipline," Trotz said. "Our work ethic was there, we had a lot more detail and I thought in the regulation, the majority of the play we had the better chances. We just couldn't convert."
At least not until Suter's bank shot, which ended a franchise playoff-record 119:03 scoring drought for the Predators and snapped Luongo's shutout streak of 126:11 dating back to Game 7 of the Chicago series.
"Obviously, you don't want to give up a goal late," said Luongo, who finished with 44 saves. "Sometimes it happens. We had a chance to win."
Before Suter's tying goal, the Predators were on the verge of being blanked for the second straight game despite outshooting the Canucks 36-15 through 60 minutes.
"I think you got to give them a lot of credit, they played a real solid game," Vigneault said. "Real good first 60 minutes, they didn't give us much and our execution was obviously off.
"We had four outnumbered situations in the second period and we didn't even get a shot. We had a 3-on-1 and we fanned on it. Give them credit, they played a good game."
Two nights after drawing criticism from their coach for their poor showing in a 1-0 loss in Game 1, the Predators came out strong – they outshot Vancouver 12-9 in the opening period, outhit the Canucks 18-7 and won 12 of 21 faceoffs.
Nashville got the game's second power play when Christian Ehrhoff was called for hooking 1:36 into the second period, but Vancouver turned some sloppy play by the Predators into a shorthanded goal.
Burrows, the overtime hero in Game 7 against Chicago, gave the Canucks the lead at the 2-minute mark with his fourth goal of the playoffs. Burrows' initial shot hit Shea Weber's skate, but the Canucks forward managed to get the rebound and put it past Rinne.
The Canucks were 67 seconds away from winning a pair of 1-0 games. Instead, the teams are heading to Tennessee all even – but the Predators are coming home with the knowledge that they can beat the Presidents' Trophy winners.
"It was a big game for us momentum- and confidence-wise," Rinne said.
1 - 0 VAN
1 - 1 Tie
1st OT Period
2nd OT Period