As well as Ylönen, Niku picked up his second helper of the night on the play.
Aleksander Barkov tied things up for the home side on the power play with under five minutes remaining in the middle frame, beating Sam Montembeault with a one-timer from Sam Reinhart.
Reinhart contributed to the Panthers' scoring efforts once again in the period, feeding Frank Vatrano with a precision pass in the crease which Vatrano tapped in to give Florida a 3-2 lead with 2:30 to go in the second.
That's where things stood after 40 minutes, with the Panthers leading 36-21 in shots.
Florida padded its lead early in the third, when Sam Bennett deflected Mackenzie Weegar's point shot just 15 seconds into the period to make it a 4-2 game.
Mason Marchment gave his team a three-goal lead when he opted to shoot on a 2-on-1 with 6:56 left in regulation, sealing the deal for the Cats.
The Canadiens play next on January 12 against the Boston Bruins at TD Garden.