"This is the start of a road trip and that's a good team over there," Montour said. "There's a chance we might see them again come playoff time, so we wanted to bring a good effort."
Evan Rodrigues and Aleksander Barkov each had a goal and an assist, and Anton Lundell had two assists for Florida (41-16-4), which has won four straight and 10 of 11.
Sergei Bobrovsky made 21 saves for his second shutout of the season in Detroit. He made 22 saves in a 2-0 win here on Nov. 2.
It was also the 10th straight start he has allowed two goals or fewer.
"[Bobrovsky] is incredible," Rodrigues said. "It's nice because your defense can be aggressive and your forwards can be aggressive. If you make a mistake, you know he's back there to bail you out."
Alex Lyon made 33 saves for Detroit (33-22-6), which has lost two in a row after a six-game winning streak.
"If we want to stay in this (playoff) battle, we have to keep getting points when we are on a roll. We did that with the six-game streak," Red Wings coach Derek Lalonde said. "But the biggest thing is to stop these momentum slides. We're in a little hole now going to Colorado (on Wednesday)."