With the win, the Flames improve to 25-18-10 on the year.
The Sabres opened the scoring with a powerplay goal at 7:56. With Brett Ritchie in the box for cross-checking, scoring sensation Tage Thompson unleased a wicked one-timer from the bottom of the far circle that whistled past Jacob Markstrom's glove and off the back bar in the blink of an eye.
Thompson - who missed the NHL All-Star Game due to an upper-body injury suffered in Buffalo's last game before the break - now has 35 goals on the year.
The Flames had a 6-2 edge on the shot clock at the midway point of the period, but it felt like the homeside had some extra jump and were slowly taking over the game with a decided territorial advantage.
Before long, the additional zone-time turned fatal for the visitors, who surrendered the 2-0 goal off the stick of Casey Mittelstadt at 12:34. Mittelstadt took a pass from Victor Olofsson off the rush and showed great patience, forcing the defenders to collapse before backpedalling into the right circle and picking the far side on Markstrom.
It was a tough break for the Flames puck-stopper, who wasn't overly busy in the period, but looked sharp early on with a big stop off Tyson Jost, who led a 3-on-1 following a defensive breakdown. Markstrom finished with 21 saves to halt a personal five-game slide.
Shots on goal favoured the Flames 11-3 after one.
Andrew Mangiapane had the best chance of the period for the Flames after taking a stretch pass from Noah Hanifin and breaking in alone, but his forehand deke clanked off the post behind Sabres netminder Ukko-Pekka Luukkonen.
Turns out, it was a sign of things to come.
Pelletier's goal came at 2:17 of the second, hustling his way up the ice to meet a beautiful, soft-area dish from Kadri, who put it right on the tape. Pulling away from a diving Olofsson, Pelletier put a beautiful shot over the blocker for the landmark tally.
"I was like, 'Come on, Pelts. Come on", man, let's go!" Pelletier said of his nearly 200-foot- gallop of the ice. "The past three or four games, I think I've had some good chances. Couldn't score. So tonight, it feels pretty good, yeah."
Backlund evened the score just 20 seconds later, cutting in from the half wall and around Rasmus Dahlin, before snapping the puck far side for his 10th of the season.
Gilbert was next up, stepping into a slapshot after taking a drop pass from Dillon Dube at 4:04. It was Gilbert's first goal as a Flame and second of his NHL career after getting one with the Blackhawks in the 2019-20 season. Elias Lindholm recorded his 300th career assist on the play.
The first three goals came only 1:47 apart, before Kadri rounded out the offence with a tip of a Huberdeau shot at 7:39.