NASHVILLE - Paul Stastny says his father Peter still talks about the overtime goal he scored in Game 7 for the Quebec Nordiques against the Montreal Canadiens in the 1985 playoffs.

While not quite as dramatic, the younger Stastny provided a performance on Thursday that Winnipeg fans won't soon forget.

The veteran centre had two goals and an assist, Connor Hellebuyck made 36 saves, and the Jets defeated the Nashville Predators 5-1 in Game 7 to advance to their first Western Conference final.

"As you get later in your career, you've just got to enjoy these moments," Stastny said. "You're going to have some guys that get nervous out there and that's fine.

"It's our job, older guys, veteran guys, to go out there and try to be loose and try to make everyone comfortable."

The 32-year-old, who waived his no-movement clause to come to Winnipeg from the St. Louis Blues prior to the trade deadline, finished with five goals and five assists in the series.

That output is even more impressive when adding in the struggles his young wingers - Patrik Laine and Nikolaj Ehlers - went through for long stretches.

"He's produced big numbers," Jets head coach Paul Maurice said. "His hockey sense is just off the charts on how to play under guys, when to get above them, when to make a play, when to not make a play."

Stastny improved to 3-1 in four career Game 7s and upped his point total in those winner-take-all affairs to four goals and four assists.

"I'm comfortable in these games," he said. "I'd rather have (the puck) on my stick."

Mark Scheifele also scored twice, including one into an empty net, while Tyler Myers had the other goal for Winnipeg. Kyle Connor and Blake Wheeler each had two assists.

"It was just great to see our group play our game," Wheeler said. "That was our goal coming into this one, that win or lose, we wanted to play our game."

P.K. Subban replied for the Predators.

Pekka Rinne allowed two goals on seven shots before getting the hook for Nashville midway through the first period. Juuse Saros made 14 saves the rest of the way.

"I feel very much responsible for our season ending at this point," Rinne said. "Tough to swallow, tough to understand."

The Jets, meanwhile, don't have much time to soak of up the victory.

Winnipeg hosts the expansion Vegas Golden Knights on Saturday in Game 1 of the Western Conference final.

Back in Winnipeg, fans crowded downtown, breaking into a rendition of O Canada while also chanting: "We Want the Cup!"

"We'll enjoy it tonight," Scheifele said. "Then back to business."

In a roller-coaster slugfest of a series where neither team was ever able to really impose its will on the other for more than a period or two, Winnipeg jumped out to a 1-0 lead on a bad-angle shot from Myers at 8:41 of the first.

The big defenceman pinched down the boards and fired a puck from the goal line that somehow snuck between Rinne's skate and the near post for his third of the playoffs.

The Jets further stunned the previously raucous crowd at Bridgestone Arena just 2:06 later on another stinker from Rinne when Stastny followed up his own rebound at the side of the Nashville net to chip home his fifth after the Predators netminder came off the near post.

That spelled the end of the night for Rinne - a Vezina Trophy finalist pulled for the third time in the series, and fourth time in this post-season.

"Total ups and downs throughout the playoffs," Rinne said. "The biggest moment of the season, it's a terrible feeling. You let your teammates down, and that's what happened tonight. That's tough to swallow."

Hellebuyck, also in the running for the Vezina as the league's top regular-season goalie, made a couple of big stops early, but Nashville responded on its second power play at 15:54 when Subban one-timed his fourth of the series, and fourth of the playoffs.

The Jets, who only got one shot on Saros the rest of the first after Rinne was pulled, had a couple of opportunities in the second when both Stastny and Bryan Little were stopped from in close.

Hellebuyck then made two big stops before Scheifele made it 3-1 with 2:10 left in the period when he took a feed from Wheeler and wired a shot past Saros.

The Predators pushed to open the third, but the Jets, who won a league-best 42 games in the regular season when leading after 40 minutes, made it 4-1 on Stastny's second of the night with 8:01 left while on the power play.

Scheifele then iced it into an empty net to take the outright lead in playoff goal-scoring with his 11th, including seven against the Predators, as Winnipeg picked up its third regulation victory of the series in Nashville - where the Predators were 25-9-7 in the regular season.

Last year's Stanley Cup finalist, Nashville fought off elimination in Winnipeg on Monday by picking up a 4-0 victory on Rinne's 34-save shutout, the third time the Predators rebounded from a loss in the series to tie things up.

But in a razor-thin matchup where neither side won two straight, Winnipeg delivered the decisive blow to book the city's first-ever trip to a conference final as the visiting team finished the series with a 5-2 record.

"It's a long journey," Hellebuyck said. "It's a lot of hours, a lot of working hard. The chemistry in this locker-room is just incredible.

"Everyone's fighting for each other."

The old Jets only advanced to the second round twice, getting swept by Edmonton in both 1985 and 1987, before relocating to Phoenix in 1996. This incarnation moved to town from Atlanta in 2011, but was beaten in four straight by Anaheim in 2011 in its only other playoff appearance.

The Predators and Jets finished the regular season with the two best records in the NHL - Nashville won its first Presidents' Trophy with 117 points, while Winnipeg was right behind with 114.

"We are just thrilled and we're pretty pleased to knock off a team like Nashville," Wheeler said. "That was every bit the series we expected it to be."

Notes: The Predators had 16 players in the lineup with at least one Game 7 under their belt. The Jets had just five including backup goalie Steve Mason. ... Thursday was the first Game 7 in Jets/Thrashers history.