Coleman tapped in a rebound on Matt Coronato's initial shot 3:08 into the third period to cut it to 2-1, and Kelly extended the lead to 3-1 at 5:55 when he corralled a centering pass from behind the net from Ross Colton and shot over Wolf's glove.
Andersson's slap shot on the power play hit Huberdeau in the shoulder in front of the net and popped over Wedgewood to trim the lead to 3-2 at 16:22.
"We didn't quit," Coleman said. "I liked the response in the third. I thought we were the better team in the third, but that was just too little, too late."
Nichushkin scored into an empty net from his own zone with 1:39 remaining for the 4-2 final.
"Management showed they had faith in us with what they did at the deadline," Wedgewood said. "I think the room knew what we had, and once you bring in the bodies that we did and the depth down the middle it really kind of turned the tide to a full confidence boost around the room. We started playing with some confidence, grabbing points and we need to continue to do so."
NOTES: Calgary had four shots in the first 32:50 and 20 shots in the remaining 27:10 of the game. ... Kelly's only other multigoal game in the NHL came as a member of the Ottawa Senators in an 8-5 loss against the Arizona Coyotes on March 5, 2022. ... Coleman's third-period goal ended a shutout streak of 125:04 for Wedgewood. ... Avalanche forward Joel Kiviranta, who had four shots, had an NHL career high four-game goal streak end (four goals). ... Flames forward Connor Zary served the first of a two-game suspension for elbowing defenseman Elias Pettersson in a 4-3 shootout loss to the Vancouver Canucks on Wednesday.