NEW YORK -- Ottawa Senators coach Guy Boucher said his team has learned from every game throughout the postseason.

Those lessons were on display Tuesday night as the Senators advanced to their first conference final since 2007.

Erik Karlsson once again played like an MVP, registering a goal and an assist, while goaltender Craig Anderson stopped 37 shots in the Senators' 4-2 victory against the Rangers at Madison Square Garden in Game 6 of their second-round series.

The Senators won the best-of-seven series 4-2 and play the winner of the series between the Washington Capitals and Pittsburgh Penguins, which concludes with Game 7 on Wednesday night.

In Games 3 and 4 at New York, the Senators were thoroughly dominated, especially at the start of both games. Coming off an overtime win at home in Game 5, one that wasn't much different than the overtime win they had in Game 2 before the series shifted to New York, the Senators took command at the start and never let go.

"We didn't have two good games here," Boucher said of Games 3 and 4. "The players reloaded emotionally, mentally and physically for (Game 5), and we wanted to do the same in this game. We wanted to be better than we were both times we played here, and that meant the first period. We wanted to come out 0-0, 1-0 or only one behind and making sure we could build our game after that.

"They managed it extremely well."

The Senators exceeded Boucher's expectations, leaving the first period with a 2-0 lead on goals from Mike Hoffman and Mark Stone. The Rangers had six minutes of power-play time in the first period but failed to capitalize with the man advantage.

When the Rangers cut the lead to 2-1 midway through the second period on Mika Zibanejad's breakaway goal, it took less than three minutes for Karlsson to respond with a goal that restored the two-goal edge and proved to be the winner.

"We had to fight every game, even though we weren't playing the way we wanted in the third and fourth game," Karlsson said. "We have a long way to go here."

New York's Chris Kreider scored on a breakaway 53 seconds into the third period to cut the Senators' lead to 3-2, but the Rangers could not find the tying goal. Anderson stopped the final 14 shots he faced, which allowed Jean-Gabriel Pageau to score his sixth goal of the series into an empty net with 6.2 seconds remaining to seal the victory.

"We came out slow," Rangers captain Ryan McDonagh said. "It's as simple as that. We were all pretty focused in here, saying the right things. But it's a difference between saying and doing, and that showed up on the ice."

Goaltender Henrik Lundqvist was the difference-maker in the Rangers' first-round win against the Montreal Canadiens as he posted a .947 save percentage over six games. In six games against the Senators, he had a pedestrian .905 save percentage.

There wasn't much Lundqvist could do on Hoffman's redirection goal, but he was beat cleanly on shots by Stone and Karlsson.

"We talked about it during the season, that it's not about playing your best game -- it's about finding a way to win games," said Lundqvist, who finished with 22 saves Tuesday. "They did that better than we did."

The Senators trailed for much of the six games, but they won two in overtime and took the series opener on a late goal from Karlsson. With a chance to close out the Rangers, the Senators delivered their best performance of the series in Game 6.

Boucher played the underdog card in this series, and it worked like a charm, even though the Rangers finished with more points in the regular season. He will likely play that same card against the Capitals or Penguins, but Ottawa will value the extended the rest before he begins playing mind games in the conference finals.

"We'll enjoy the moment," Anderson said, "but at the end of the day, we've still got to look forward and move forward. The job is not finished."

NOTES: The Senators used the same lineup in Game 6 as they did in Game 5, which included RW Chris Neil. He had zero shots in 1:49 of ice time. ... The Senators allowed two power-play goals in 24 chances during the series. ... The Rangers scratched LW Pavel Buchnevich in favor of LW Tanner Glass for the fourth straight game. Glass had one shot and was minus-1 in 8:34 of ice time. ... Rangers G Henrik Lundqvist lost for only the second time in 12 starts with his team facing elimination at home.