Artemi Panarin and Mika Zibanejad each had a goal and an assist, and Igor Shesterkin made 28 saves for the Rangers (19-8-4).
"I was real happy with the first two periods, obviously," New York coach Gerard Gallant said. "I thought it was a good game, both teams back and forth, good goaltending, good solid play from both teams. In the third, we got away from it and made a couple of mistakes and they ended up in the back of the next."
Verhaeghe gave Florida a 3-2 lead at 10:31 when he ended an eight-game goal drought with a wrist shot from the top of the left circle. Anthony Duclair made it 4-2 at 14:40 when he finished a rush he began by blocking a shot inside the Florida zone.
"I was extremely happy for him," Panthers coach Andrew Brunette said. "It was a huge block and he scored a huge goal for us. I was proud of him. It was good to see him put his body on the line for the group and score a big goal."
Chris Kreider scored for the Rangers at 19:15 for the 4-3 final.