Jonathan Huberdeau scored 17 seconds into the game, and Brett Connolly scored his 100th NHL goal for the Panthers (23-9-4), who have won three in a row following a three-game losing streak. Sergei Bobrovsky made 35 saves.
Verhaeghe has scored five goals in his past three games. He scored a hat trick in a 4-3 overtime win against the Dallas Stars on Saturday.
"There's a lot of games, so you get a lot of puck touches and everything, so you're kind of feeling confident with the puck," Verhaeghe said. "But, yeah, the team has been doing well. We're on a three-game win streak here, which is nice after a three-game losing streak, and it shows the resilience of the team for sure."
Filip Zadina scored for the Red Wings (12-21-4), who failed trying for their first three-game winning streak of the season. Calvin Pickard allowed three goals on eight shots in the first period before being replaced by Thomas Greiss, who made 24 saves.
"It's as bad as we've played defensively in a while," Detroit coach Jeff Blashill said. "We weren't at our best. We had a bunch of guys that played their B and C games."
This first game of a two-game set here was Florida's first without defenseman Aaron Ekblad, who will be out 12 weeks after having surgery Monday after breaking his left leg in a 4-1 win against Dallas the previous night.
The Panthers also were without forwards Aleksander Barkov and Patric Hornqvist, then lost forward Anthony Duclair to an apparent shoulder injury in the final seconds of the second period. Panthers coach Joel Quenneville said after the game that Duclair would be out 7-10 days.
"We [were] short, we missed a few guys, a few key guys, but I think it's also opened up the opportunity for other guys to play bigger roles, play bigger minutes and earn their spot in the lineup," Bobrovsky said. "It's good, and it's also some adversity for us to overcome to get together and be strong."