Zibanejad scored his first goal on a power play at 14:36 of the first period and gave the Rangers a 2-0 lead with his second midway through the middle period.
That goal appeared to roust the Panthers, who scored twice in the period, yet trailed 3-2 going into the third.
“I thought we had a real good first period, real solid,” New York coach Gerard Gallant said. “We controlled the play, played the way we wanted to.”
Cousins put Florida on the board at 13:57 of the second before Kreider made it 3-1 at 15:44.
Bennett’s power-play goal with under a minute remaining in the second period gave the Panthers a lift and snapped an 0-for-9 drought with a man advantage dating to a loss at Carolina on Friday night.
Trocheck, who was drafted by, and spent his first seven NHL seasons with, the Panthers, gave the Rangers a two-goal cushion again when he tapped in a pass from Kreider on a power play at 1:38 of the third.
“It’s always nice to beat these guys,” said Trocheck, who ended with two points in the win. “I did not leave too long ago but in the COVID year, I played them eight times. So I have played them a ton already. It’s not as fresh as it was the first couple of times, but it is nice.”
Florida closed within a goal when Staal scored his fourth goal of the season just over a minute later.
Panarin restored the Rangers’ two-goal cushion at 10:04of the third, making it 5-3.
“I don’t think our game changed a whole lot playing from behind,” Florida coach Paul Maurice said. “We did not move the puck well, it was in the feet and it ended up in the back of our net a couple times. … (The Rangers) did not get a lot but they finished. They have good shooters there.”
NOTES: The Rangers had Alexis Lafreniere back in the lineup after he was a healthy scratch Friday night in Tampa. Lafreniere was on the third line with center Filip Chytil and Jimmy Vesey. … The three coaches on the New York bench had ties to the Panthers. Gerard Gallant was head coach in Florida for parts of three seasons (2014-16), along with assistant Mike Kelly. Gord Murphy was an original member of the Panthers as a defenseman and was also an assistant coach. … Florida had Zac Dalpe back in the lineup after playing Anton Levtchi the previous two games. Levtchi was returned to AHL Charlotte on Saturday.
Rangers: Host Carolina on Tuesday night.
Panthers: Host Arizona on Tuesday night.
AP NHL: https://apnews.com/hub/nhl and https://twitter.com/AP_Sports
George Richards, The Associated Press