Backlund followed up with a power play marker at the 17:20 mark of the second period when he slid the puck past a maze of bodies and past Pickard to increase the Flames lead to 2-0.
It was Backlund's sixth goal and ninth point in his last five games and Matthew Tkachuk picked up an assist, extending his point streak to a career-high seven games.
The goal marked Backlund's 200th career NHL point.
"It was a nice milestone to hit. Looking back when I was drafted, you never knew if you were going to get to play 400 games and get 200 points," Backlund said. "It's a step out of the way and I want to try to keep getting better and try to keep doing that."
Chiasson gave Calgary a 3-0 lead 6:35 into the third period when Brodie was tripped up but still managed to chip the puck to Chiasson, who blasted home his sixth of the season.
"Brods has some of the best perception in the game," Giordano said of his former blueline partner. "He got tripped up and still got it to the front of the net.
"It was nice to see Chiasser get rewarded because he has been working really hard for us and doing a lot of things for us that go unnoticed."
Gaudreau completed the scoring for the Flames while on a five-on-three advantage. The slick forward picked up the puck and skated around the back of the net but made a sharp hairpin turn to open up some net and slide the puck past Pickard.
"Our team game was really good tonight but our special teams ... our power play really pushed us over the top tonight," Giordano said. "We generated a lot of chances, we had a lot of looks and put three goals in the net.
"Any time you put three in on eht power play you're not going to lose many of those games, unless it's a high-scoring game."
Wiercoich ruined Elliott's shutout bid in the final two minutes when he flipped a weak backhand towards the goal that Elliott misplayed and gave Colorado their only marker of the contest.
NOTES: Scratched for the Flames was defenceman Jyrki Jokipakka (healthy) and forwards Troy Brouwer (broken finger) and Garnet Hathaway (healthy).
UP NEXT: The Flames travel to Vancouver for the front end of a home-and-home set against the Canucks on Friday (8:00 PM; SNW, SN960).