The Rangers shook off a 5-2 thrashing in Philadelphia on Tuesday and knocked out the Flyers about 24 hours later, improving to 6-0 in Game 7s at Madison Square Garden. New York will face another Metropolitan Division rival, the Pittsburgh Penguins, in the next round starting on Friday.
Henrik Lundqvist made 26 saves, allowing only a third-period goal to Jason Akeson 3:32 into the final frame. He protected the one-goal lead at 7:25 when he made an awkward save against Flyers captain Claude Giroux.
The Rangers mobbed Lundqvist after the final buzzer, while the Flyers consoled their goalie Steve Mason.
Mason, who didn't start until Game 4 because of injury, was sharp in stopping 31 shots, but he couldn't will his club to a complete comeback after the Flyers fell into a 3-2 series hole. The Flyers dropped to 9-7 in Game 7 after winning their previous three.
No team won consecutive games in the series. The Rangers, who finished two points ahead of Philadelphia during the regular season, made the most of their home-ice advantage by taking three of the four games in the Garden.
Carcillo, re-inserted into the Game 7 lineup, scored the all-important first goal 3:06 into the second off a picture-perfect pass from Mats Zuccarello.
Zuccarello threaded the puck with a behind-the-back feed from near the right circle between the legs of Flyers defensemen Andrew MacDonald and Braydon Coburn to Carcillo for the redirection into the net.
It was the second goal of the series for Carcillo, who played for just the third time in the series and the first at home. Carcillo had come out of the penalty box less than a minute earlier after serving a penalty for too many men on the ice.
The Rangers nearly doubled the lead later in the frame when they mounted a flurry of pressure in the crease, only to be stymied by Mason and done in by errant whacks at the puck.
But Philadelphia couldn't capitalize on that mistake or on two power plays in the period in which the Flyers were outshot 18-5.
New York did grab a 2-0 lead with 8:14 left in the second when Pouliot also turned a crisp pass into his second goal of the series.
Derick Brassard sent the puck from the right-wing boards into the slot and appeared to be aiming for defenseman Marc Staal, but Pouliot streaked down the middle, snared the puck and steered it past Mason to send the once-nervous crowd into a towel-waving frenzy.
The Flyers held an 11-10 shots advantage in the first scoreless opening period of the series.
New York again failed to capitalize on the lone power play in the frame, stretching its streak of futility to 21 straight advantages. When the Rangers did put pressure on Philadelphia, Mason stood tall just as he did in winning Game 6 at home on Tuesday night.
Rick Nash, still searching for his first goal of the series, nearly got it when after a Flyers turnover created a chance for him from the slot. But his drive was knocked away by Mason, who stretched out his gloved hand to deflect it.
Nash also struck a goal post in the first minute of the game.
Lundqvist matched Mason at the end as the Flyers had several stretches of puck possession within the Rangers zone. His best stop came when Matt Read let go a screened shot 4 minutes in.
NOTES: Carcillo replaced J.T. Miller, who had played in the previous two games of the series. Carcillo is 3-0 in career Game 7s and has scored in two of them. Carcillo had four goals in the regular season in 57 total games with Los Angeles and the Rangers. ... This was the only first-round series that didn't require overtime in any game.