Nylander scored the first of his three goals 32 seconds after the opening faceoff and paved the way for the Rangers' 7-0 blowout Tuesday that put New York within a win of the second round of the playoffs for the first time in a decade.
"Nobody on this team played 10 years ago," said Jagr, who had four assists. "We just want to win the game and play the same way."
Lehtonen got the curious start over Johan Hedberg and then endured a thorough beating as the Rangers scored three times in the first period and cruised to a commanding 3-0 lead in the Eastern Conference playoff series.
Nylander had his first playoff hat trick, and Henrik Lundqvist stopped 21 shots in his first NHL playoff shutout for the Rangers, who can advance to the second round as early as Wednesday at home.
"It felt like everything was working for us," Lundqvist said. "It's not every night, especially not in the playoffs, when everything just seems to work for you."
Tell that to his young counterpart.
Lehtonen was touched for all seven goals on 35 shots. That was enough for the Rangers' victory theme "Sweet Caroline" to play with 5:16 remaining over chants of "Sweep! Sweep!"
"It's the time when you really want to make the difference and you want to make them mad when you're playing in a place like this," Lehtonen said. "But today they are happy."
Jagr assisted on all of Nylander's scores and they teamed to set up defenseman Marek Malik for another that made it 3-0 at 12:26.
But Nylander's first strike was the quickest.
"It's something that you don't want, but I was able to put it behind me right away and focus on the next shift," Lehtonen said. "It's what I always do but they kept coming hard and we didn't make it tough enough."
Thrashers coach Bob Hartley, who went back to Lehtonen -- the Game 1 loser -- even though Hedberg played well in Game 2, called timeout after Malik's goal. Lehtonen skated to the bench to regroup while Hedberg took a calm squirt of water.
The break only brought temporary relief to Lehtonen and the Southeast Division-winning Thrashers, who are on the brink of a sweep in their first playoff appearance.
"How can we blame Kari?" said Hartley, who said his team froze after the early goal. "No. 1, we don't score, so at best we would still be playing. Kari Lehtonen is a young goalie. He played hard, he played very well for us but he was by himself on the ice."
A year ago, the Rangers were swept on their return to the postseason after missing seven straight times. Jagr and Lundqvist were hurt and New York was no match for New Jersey then, but this group earned the team's first home playoff win since 1997.
Red, white and blue balloons fell from the upper reaches of the Garden during the national anthem, and the loud din hadn't left the arena when Nylander scored.
Lehtonen stopped 34 of 38 shots in the series-opening 4-3 loss and was worse upon his return.
"There are no answers," forward Bobby Holik said. "The passion should be there but it isn't."
Hedberg made 37 saves in a much better performance Saturday, allowing a fluke goal on Sean Avery's bank shot from center ice and Shanahan's gimme off a perfect setup in front by Avery in the 2-1 defeat.
But Hartley announced Monday that he was going back to Lehtonen, the No. 2 overall pick in the 2002 Draft and Atlanta's presumed goalie of the future.
It didn't work.
The skating and zigzagging play by Jagr and Nylander looked every bit like the Harlem Globetrotters on ice.
Jagr eluded Eric Belanger in the neutral zone then found Nylander behind the Thrashers' defense for the first goal. Nylander then got to a big rebound of Marcel Hossa's shot in the right circle to make it 2-0 at 9:45. When Malik scored 2:41 later, the only question left was how long Hartley would stick with the 23-year-old Lehtonen.
The only reason he wasn't pulled was Hartley didn't want to spend Hedberg, who'll start Game 4.
Callahan, who netted four goals in 14 games, got two postseason tallies just under 11 minutes apart in the second period to bust the game open.
Lundqvist's biggest test came during a Rangers power play late in the first period when Pascal Dupuis, who played briefly with New York this season, got free on a breakaway but had the puck slide off his stick. Lundqvist also flopped flat on his back in the second to keep Atlanta off the board.
- Nylander's hat trick was the Rangers' first in the playoffs since Wayne Gretzky on May 18, 1997.
- Tyutin had 12 assists in the regular season.
- Lehtonen allowed a season-high five goals in a game five times.
- The Rangers have a 112-73 shots advantage in the series. Atlanta recorded three in the third period.