Brad Richards, Michael Del Zotto, and Brandon Dubinsky also scored for the Rangers, who have won six of seven and will play the Philadelphia Flyers in the Winter Classic on Monday in Citizens Bank Park.
Ryan McDonagh had two assists for New York, which leads the Eastern Conference with 50 points.
Matt Bradley scored for the Panthers.
With 7.6 seconds left in the game, Del Zotto delivered a cross-check to Tomas Kopecky in front of the net knocking Kopecky's helmet off.
Kopecky responded with a punch that knocked Del Zotto to the ice. The incident prompted a fight with Kopecky and Mike Rupp.
It didn't take long for the Rangers to score.
Later in the first period, Richards beat Clemmensen with a wrist shot and Del Zotto scored from the blue line ending Clemmensen's night. Clemmensen stopped 11 of 14 shots before being replaced by Jose Theodore.
Dubinsky gave the Rangers a 4-0 lead in the second period on an impressive goal as he weaved through traffic and fired a backhand by Theodore for his fourth of the season.
Lundqvist was sharp throughout, stopping seven shots in the first, 11 in the second and nine in the final period.
Theodore turned away 10 of 11 shots for the Panthers, who have lost four of five.
Notes: Hagelin has scored four goals in the past six games. ... Michael Del Zotto was a plus-2 giving him a plus or even rating in 30 of 36 games for the Rangers. ... The Rangers waived F Sean Avery prior to the game. ... Panthers F Stephen Weiss had four shots in his return to the lineup after missing two games due to an upper body injury. ... The loss for Clemmensen (3-1-2) was his first of the season in regulation.