TAMPA -- The meeting that helped save the New York Rangers season took place Tuesday morning in the cramped quarters of the visiting coach's room inside Amalie Arena.

Rangers coach Alain Vigneault called in centers Derick Brassard and Derek Stepan and presented them with a challenge.

"He challenged us to be a little better," Brassard said.

It was just the three of them. No voices were raised. Nothing crazy happened. No hard feelings. No animosity.

"We never felt he was angry with us, but it was good to have that little extra push," Stepan said.

Vigneault gave it to them because he knew that there was no way the Rangers were going to survive one more night in the 2015 Stanley Cup Playoffs without a strong performance from their top two centers, or at least one that was stronger than they had in Game 5, when New York got shut out 2-0 at Madison Square Garden.

Stepan took it as a confidence-building message from the coach.

Brassard took it to heart. He answered with the best game of his NHL career.

Brassard scored a hat trick and had two assists for a five-point night in New York's 7-3 victory against the Tampa Bay Lightning that set up a Game 7 on Friday at Madison Square Garden (8 p.m. ET; NBCSN, CBC, TVA Sports), where the Rangers don't lose Game 7s; they are 7-0 all-time in Game 7s at the Garden.

Brassard, who had 10 shots on goal and a plus-5 rating, had the first Rangers hat trick when New York was facing elimination since Mark Messier did it after famously guaranteeing a victory in Game 6 of the 1994 Eastern Conference Final against the New Jersey Devils.

It was the first Rangers hat trick in a road playoff game since Wayne Gretzky in 1997. Before Tuesday, the last Rangers playoff hat trick came from Michael Nylander in 2007.

Brassard also became the first player in Rangers history to have at least five points in a playoff game with New York facing elimination.

"Since I've been playing hockey in junior, every time I get challenged like that, I always try to answer," Brassard said. "I was already hard on myself, and it kind of got me more mad [Tuesday] morning."

The Rangers discovered an angry Brassard is a better Brassard. Maybe Vigneault knew it all the time.

"I was disappointed the way I played last game," said Brassard, who was held to two shots on goal and six shot attempts in Game 5. "It was a pretty [bad] feeling [Monday], and I just tried to step up there for the team."

Brassard gave New York a 1-0 lead at 3:36 of the first period. He had an assist on Keith Yandle's goal that gave the Rangers a 2-0 lead at 15:30 of the first.

The Rangers struggled to establish much of an attack in the second period as the Lightning came at them in waves, odd-man rush after odd-man rush. Brassard still managed three shots on goal in the period; his line, with J.T. Miller and Rick Nash, was the only one generating anything for the Rangers. They were on the ice for eight of New York's 11 shots.

Brassard came out in the third period and led the Rangers' push that turned into a domination.

He set up Miller for a goal at 3:02 after Lightning goalie Ben Bishop denied him with a remarkable flailing save. Instead of showing frustration, Brassard stuck with the play, collected the puck behind the net, and found Miller in the slot.

Miller found Brassard wide open in the right circle for a shot that he deposited into the back of the net at 7:14 to give the Rangers a 5-1 lead.

Brassard was on the ice when Nash scored his power-play goal at 10:21, and then completed his hat trick with an empty-net goal at 18:19.

Brassard's line had 13 points in Game 6, including four each from Miller and Nash.

"Brassard's line was obviously unbelievable," Vigneault said.

Brassard is developing a reputation as the Rangers' big-game forward in the same way goalie Henrik Lundqvist already has the reputation as arguably the best big-game goalie in the NHL to never win the Stanley Cup.

Brassard has 13 points, including six goals, in the 10 games the Rangers have played when facing elimination since last year. New York is 9-1 in those games.

"Honestly, I just go out there and I try to just make a difference," Brassard said. "When I feel like the team needs some support offensively or I feel I need to step up, I just try to do it. I don't really put any pressure on myself."

Brassard said after Game 5 his memories of losing in the Stanley Cup Final came rushing back. It was hard to deal with, and he admittedly had a rough day Monday.

"The disappointment from losing last year I think really hit me from losing the last game at home and facing elimination tonight," Brassard said. "We're not far away to be in the Final again. I just play."

He apparently plays better when he's challenged.

"You saw how he played tonight," Stepan said. "He was our best player."

Challenge accepted.

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