Nathan MacKinnon and Tyson Barrie had a goal and an assist each as the Avalanche (34-24-5) avenged a 5-1 loss to the Flames in Calgary on Saturday afternoon.
Backlund also had an assist for the Flames (32-24-9) for a two-point outing, while goalie David Rittich made 29 saves.
"I liked the way our guys played in the third," said coach Glen Gulutzan in regards to his players outshooting the Avs 13-5 in the final frame. "They were an angry group. We just couldn't break through. This has got to unite us and galvanize us as we head into our last 17 games."
Nikita Zadorov, Matt Nieto and Duncan Siemens also scored for Colorado, while Carl Soderberg and former Flame Blake Comeau chipped in with two assist each. Netminder Semyon Varlamov finished with 30 saves.
Just 59 seconds into the game, the Flames appeared to open the scoring when the puck crossed the line after Sam Bennett drove hard to the net, but the goal was waved off immediately due to goalie interference.
Backlund put Calgary up 1-0 with a shorthanded goal at 14:19 of the first period. After Colorado defenceman Tyson Barrie mishandled the puck at the point, Backlund snuck in behind him and skated into the Colorado zone on a breakaway before making a quick move and backhanding a shot past Varlamov.
The Flames extended their lead to 2-0 at 2:41 of the second when a hard pass from Backlund bounced off Matthew Tkachuk's stick and right out front to Frolik, who backhanded a shot past Varlamov.
MacKinnon and Zadorov then answered back for Colorado with a pair of goals 68 seconds apart before the mid-way mark of the second stanza.
"They got some momentum there in the second," said Calgary captain Mark Giordano. "They got a powerplay goal and then they kept coming. They didn't stop and got the lead. We had some looks, but we couldn't really put that third one in to get some pressure on them."
Barrie gave the Avs their first lead of the game at 12:41 of the second when he finished off a nice three-way passing play by one-timing a pass from Mikko Rantanen past Rittich.
Nieto doubled Colorado's lead with 1:18 remaining before the second intermission by backhanding a perfect pass from Carl Soderberg past Rittich for his 100th career NHL point.
The Flames had to play the majority of the final frame without the services of leading scorer Johnny Gaudreau, who was assessed a minor penalty for embellishment and a 10-minute misconduct after taking a high stick from Comeau at 8:05 of the third.
"That one to me is dumbfounding," Gulutzan said. "I've got to defend my guy here. This is our guy. This is our best player. He gets high-sticked in the face and minutes later he's thrown out of the game. I don't know how you're supposed to react to getting hit in the face."
Dougie Hamilton, who hit a crossbar one night earlier in Calgary's 2-0 road loss to the Dallas Stars, rang a shot off the post during a powerplay for the Flames shortly after Gaudreau left the game.
The Flames continued to press hard to score in the third period, in which they outshot the Avs 13-5, but they weren't able to get any more pucks past Varlamov.
"I thought that everybody was pretty much on the same page on wanting to come back and get that win, but it just didn't happen," Tkachuk said.
Siemens sealed the victory for the Avs by scoring into an empty net for his first NHL goal.
