Predators beat Flames 5-3
Kevin Klein and Matt Halischuk also scored for Nashville.
Jarome Iginla, Rene Bourque and Brendan Morrison scored for the Flames, who have lost three straight.
Kostitsyn's first goal gave Nashville a 2-1 lead. His second made it 4-1 and he capped the scoring with an empty-net goal.
Iginla, stationed in front of the crease, beat goaltender Pekka Rinne with a wrist shot 3:47 into the game.
Klein tied the game with 7:21 left in the first period when he blasted a slap shot from the blue line that beat goaltender Mikka Kiprusoff to his glove side.
The Predators took the lead at 2-1 when Kostitsyn skated in from the right side and beat Kiprusoff to his glove side with a wrist shot from close range with 4:54 remaining in the first.
Halischuk added to the lead 2:27 into the second period with a snap shot from low in the slot.
Kostitsyn struck for the second time with a wrist shot on a 2-on-1 from the right side that went between Kiprusoff's legs at 5:59 of the second.
Calgary cut the lead to 4-2 when Bourque skated in from the left side and beat Rinne from close range 1:17 into the third period.
Morrison scored on a rebound from close range with 2:03 left to play.
With 30 seconds remaining Kostitsyn scored an empty-net goal.
NOTES: Calgary's Olli Jokinen played in his 1,000th career NHL game. ... Klein was removed from injured reserve and returned to the lineup against Calgary after missing six games with complications from the flu. ... Nashville's Jordin Tootoo was credited with two assists, giving him 15 points (six goals, nine assists) in his last 18 games. ... Iginla, who has eight goals and 11 assists in his last 16 games, is one goal short of 500 for his career. ... Nashville's Patric Hornqvist also had two assists.