Adam Fox had a goal and two assists, and Jimmy Vesey, Alexis Lafreniere and Filip Chytil also scored for the Rangers, who are 15-4-2 since Dec. 5 and 5-0-1 in their last six home games against Florida. Artemi Panarin had three assists.
Carter Verhaeghe and Aleksander Barkov scored for the Panthers, who had won four of their previous five and are 7-3-1 since Jan. 1, when the Rangers won the previous meeting 5-3 in Florida.
Shesterkin had seven saves in the first, 14 in the second and 12 in the third to improve to 11-4-3 in his last 18 starts and 21-8-6 overall this season.
The 27-year-old Russian just missed scoring when the Panthers pulled goaltender Alex Lyon with more than five minutes left, down by three goals. Sheskterin’s full-rink attempt missed wide left by mere inches.
Fox opened the scoring with his 10th goal at 3:03 of the first, bursting past the Panthers’ defense before sliding the puck past Lyon. Fox has points in 32 of New York’s 47 games this season.
Verhaeghe tied it on the power play at 5:56 with his 23rd, giving the Panthers goals with the man advantage for the fourth straight game and seven of the last eight.
Zibanejad put the Rangers ahead with 2:39 left in the first on the power play, one-timing a pass from Panarin past Lyon from his patented spot in the left circle. Fox had an assist on the play, giving him a multi-point effort for the third time in six games. The Rangers are 11-0-0 when Fox records multiple points.
Vesey made it 3-1 at 15:03 of the second with his eighth.
Lafreniere scored for the first time in 18 games at 7:56 of the third before Zibanejad scored again — his team-leading 22nd — at 8:10 to make it 5-1.
Barkov pulled the Panthers within three at 11:02 of the third with his 13th before Chytil completed the scoring with an empty-net goal with 3:11 remaining.
Panarin, who leads the Rangers with 50 points, extended his points streak against the Panthers to 12 games.
Former Rangers defenseman Marc Staal played his first game with the Panthers at Madison Square Garden after two seasons with Detroit. Staal, who was traded to the Red Wings in September 2020, played 892 games over 13 seasons in New York and skated in the second-most playoff games (107) in Rangers history.
Panthers: At Pittsburgh on Tuesday night.
Rangers: At Toronto on Wednesday night.