Kucherov cut it to 2-1 with a power-play goal at 17:39 of the second period, one-timing a pass from Steven Stamkos in the right circle.
Chris Kreider quickly responded to make it 3-1 at 18:30. He beat Vasilevskiy short side from the left circle on a 2-on-1 with Trocheck.
"That's something you talk about when you're in minor hockey, the shift after a goal is a big one, right?" Stamkos said. "It was an unfortunate play where we were a little in between. Stuff like that happens. Mistakes happen. It was tough timing, but that's the way it went tonight."
Panarin pushed it to 4-1 at 11:16 of the third period with a wrist shot from the right circle. He then completed the hat trick with a power-play goal at 15:26 for the 5-1 final.
"I feel great," Panarin said. "I don't know what can be better [than] to finish the year like that. We won the game. That is important."
NOTES: It was Panarin's second hat trick this season and sixth in the NHL. ... Rangers forward Mika Zibanejad had the secondary assist on Panarin's power-play goal to extend his point streak to 10 games (eight goals, nine assists). ... New York is the first team to reach 50 points this season. The last time the Rangers accomplished the feat was in 1993-94, when they won the Stanley Cup. ... Lightning forward Conor Sheary left in the second period with an undisclosed injury.