Montembeault stopped Duchene, Ryan Johansen and Turris in the shootout.
"I felt really good today," Montembeault said. "Going into the shootout, counting last year, I went into a shootout in [three] of my last [four] starts and haven't won in a shootout in almost two years, so it was important for me to win this one."
Denis Malgin gave the Panthers a 1-0 lead at 13:33 of the second period on the power play, taking a cross-ice pass from Trocheck and beating Rinne from low in the left face-off circle.
"I like how [Malgin] comes through the middle and he's got some speed, and all of the sudden you go through coverage and he's in the zone, and the options open up for him," Florida coach Joel Quenneville said. "But he sees the plays well. I think he's got some real speed with the puck, and I think that's dangerous."