Draisaitl responded to tie it 2-2 at 17:30. He picked up a loose puck at center ice and drove through the right circle in on Bobrovsky before beating him short side with a quick shot in tight.
The Panthers scored twice in 2:43 in the third period to take control of the game.
Schmidt took a drop pass from A.J. Greer and beat Skinner with a wrist shot from the bottom of the left circle to give Florida a 3-2 lead at 11:08, and Verhaeghe pushed it to 4-2 at 13:51 when he followed up his initial attempt and poked it in from below the left circle.
“This is always a big game, especially after what happened last year,” Verhaeghe said. “Getting the best of them tonight kind of sent a message. The way we played, we kind of grinded it out. We got the win, so that’s most important.”
Zach Hyman knocked in a centering pass from Connor McDavid with Skinner on the bench for an extra attacker for the 4-3 final at 16:35.
“It was a solid game by both teams. They are a hard forechecking team, big bodies who shoot a lot of pucks and get bodies to the net, which makes my job tough,” Skinner said. “We started to get going midway through the first period. Once we found our legs, we were pretty solid. Tough way to lose, for sure.”