Jumping out to an early lead, the Rangers opened the scoring when Adam Fox slipped through the defense before beating Alex Lyon on a breakaway to make it 1-0 at 3:03 of the first period.
Still sizzling on the power play, the Panthers, who have operated at over 40% with the extra attacker since Jan. 1, answered when Carter Verhaeghe took a pass from Anton Lundell and lifted a shot over Shesterkin's glove from the right side of the net to make it 1-1 at 5:56.
On a man advantage of their own, the Rangers regained the lead when Mika Zibanejad, who recorded a pair of goals against the Panthers back on Jan. 1, teed up a cross-ice pass from Artemi Panarin and blasted a one-timer into the net from the left circle to make it 2-1 at 17:21.
With not much time left in the opening period, the Panthers received a scare when Sam Bennett got tied up with Filip Chytil and crashed feet-first into the boards. Despite being helped off the ice by a trainer, Bennett returned to the ice and played a bit in the second period.
Even though the Panthers led 29-12 in shot attempts and 14-8 in scoring chances in the middle frame, the Rangers added to their lead when, after a few big saves from Lyon, Jimmy Vesey pushed the puck out from under a pile and across the goal line to make it 3-1 at 15:03.
At the start of the third, Bennett did come back out for the Panthers.
"It just started to tighten again," Panthers head coach Paul Maurice said of Bennett's injury. "We can't have this turn into something longer. If he's got to miss the next three [games], so be it. But then we've got a seven-day block where we can really capture some healing on it."
Pulling away in the final frame, Alexis Lafreniere took advantage of some more chaos around the net and snuck a shot past Lyon to extend New York's lead to 4-1 at 7:56. Just 14 seconds later, Zibanejad went top-shelf from the right circle for his second goal of the game to make it 5-1 at 8:10.
Lyon finished with 20 saves, while Shesterkin racked up 33.
After pulling their goaltender with just under 10 minutes left to gain a 6-on-5 advantage, the Panthers cut into their deficit when Aleksander Barkov's shot went off Shesterkin and in to make it 5-2 at 11:02. With the goal, the captain extended his point streak to eight games.
With 3:11 left in regulation, Chytil cashed in on the empty net to put New York up 6-2.
"Just missed some execution on the finish," Maurice said. "They made some saves, but I think some of our best offense we never actually got to the net. … I think they worked their [butts] off, but I don't think the hands were easy to find. You get behind it and then you're chasing it."
