The teams will meet again Thursday night in Dallas.
Kari Lehtonen made 43 saves for the Stars. Jacob Markstrom and Tyler Plante, who are competing for the backup goalie job with veteran Scott Clemmensen out 4 to 6 weeks after undergoing knee surgery, split the game for Florida.
Markstrom stopped all 10 shots he faced before being removed at 11:02 of the second period. Plante gave up four goals on 16 shots.
Ryder scored on a 2-on-1 when he took a pass from Mike Ribeiro and beat Plante with a high shot.
Dallas led 3-1 before Huberdeau and Kulikov scored power-play goals 35 seconds apart late in the third period.
Huberdeau, the third overall pick in the 2011 draft, scored on a 5-on-3 power play with 3:52 to play after Dallas' Ryan Garbutt was assessed a 5-minute major for checking Tim Kennedy into the boards from behind and Ribeiro took a double-minor.
Kulikov scored with a one-man advantage on a shot from the slot.
Florida outshot Dallas 26-3 in the third period.
Fourteen seconds after Plante entered the game, Vincour scored when a deke attempt went off his stick and the puck slid between Plante's legs.