Florida's first-period goals both came off New York turnovers. Lafreniere lost the puck in the attacking zone, leading to a rush down the ice the other way and Lundell scoring. Reilly Smith lost the puck in the defensive zone, leading to Verhaeghe's goal.
The Rangers allowed three goals in the first period in their first six games.
"We haven't been particularly defensively oriented here; tonight we would have to be," Florida coach Paul Maurice said. "I think they were at 5.17 for goals [for] per game coming in and we're missing our Selke [Trophy winner Aleksander Barkov] down the middle, so we had to play a really hard defensive game and when that happens you get some chances."
Lafreniere made it 2-1 at 4:44. Adam Fox protected the puck on the right-wing wall and found Lafreniere cutting through the left circle. Lafreniere deked to his backhand and tucked the puck past Bobrovsky.
Bobrovsky stopped Jonny Brodzinski on a breakaway at 5:45, Filip Chytil on a breakaway at 6:33 and in the slot seven seconds later, and Kreider twice in front of the net on a power play at 15:12.
His right skate save on Vincent Trocheck at 6:15 of the second period also preserved the one-goal lead and might have been his most timely save of the night.
"The puck was the right there and I just threw as much as possible [at it]," Bobrovsky said. "Luckily it hit my toe."
The Panthers scored less than a minute later. Bennett extended the lead to 3-1 at 6:59 with a high-slot redirection of Niko Mikkola's shot from the left circle.
Bennett has goals in three straight games and leads the Panthers with six. They have all come in the high danger zone, the most in the NHL from that area on the ice.
"He's taking control," Panthers forward Matthew Tkachuk said. "He's skating well with the puck. When our line is playing puck possession, give and go, supporting each other, I think we can be really effective. He's gotten off to a great start."
The Rangers had a 6-on-4 power play with Shesterkin pulled for an extra skater at 16:57 of the third period but couldn't score. They were 0-for-4 on the power play.
"I thought that they were better in the first, I thought that they were better in the second, and they were better in the third," Laviolette said. "We're better than that and we didn't play that way tonight."
NOTES: Florida played its seventh straight game without Barkov (lower body), who could return Saturday against the New York Islanders. … Rangers forward Artemi Panarinhad an assist on Lafreniere's goal to extend his point streak to seven games (six goals, eight assists). … The Rangers sent forward Matt Rempe to Hartford of the American Hockey League following the game. Rempe was a healthy scratch Thursday for the fifth time in seven games.