Paul Stastny, John Mitchell and Matt Duchene also scored for the Avalanche, who joined the 1995 Quebec Nordiques for the best 15-game start in franchise history. Colorado (13-2) needed 29 games to earn 26 points in last year's lockout shortened season.
Giguere has been a big reason for Colorado's turnaround. The 36-year-old goalie's 5-0 record ties the franchise record for best start to a season.
He came into Friday having allowed three goals in four games and posted two shutouts, so allowing two goals in a span of 3:39 seemed out of character.
"You are not going to be perfect every time," Giguere said.
Early, it looked like Colorado would cruise against the struggling Flames.
The Avalanche were up 2-0 after Stastny scored on a 5-on-3 1:09 into the second period, but Cammalleri kept Calgary close. He scored his first goal on a pass from Backlund early in the second, and 2:30 after Mitchell restored Colorado's two-goal lead, he beat Giguere again to make it 3-2 midway through the second period.
It wasn't enough to overcome another slow beginning.
"I thought it was the start again. I don't know what it is," Cammalleri said. "It seems like we're in kind of a little bit wait-and-see and then we spot them two or three and it makes it hard."
Cammalleri nearly got the hat trick on an 2-on-1 rush late in the period but Giguere made the save.
"He's a capable goaltender. He's going to make his saves," Cammalleri said. "I'm sure if you ask him on the goals he'd like to have them back and the ones he saved I'd like to have them back."
Giguere had to be sharp again in the third to keep the game from going to overtime. He stopped Cammalleri again on the power play in the first minute of the period and made 13 saves in the frame.
Jiri Hudler had a backhand chance with 2:35 left but Giguere made a sprawling save.
The Flames pulled Ramo for an extra skater with just over a minute remaining but couldn't get the equalizer. Duchene iced it with an empty-netter in the final seconds. It was his 11th goal of the season.
"I think after the first period we might have taken them lightly," Duchene said. "We dominated the first period. The second and third I thought they were skating downhill."
Colorado survived to rebound after a tough loss to Nashville on Thursday.
"This was a big game for us. After going 12-1, you lose a game, it would be easy to go into bad habits and lose some," Giguere said. "We ended up getting a big win. We should be happy with this one."
The Flames are searching for answers after another tough loss. They started the season 4-2-2 but have earned only four points in their past nine games.
"We had some real bad turnovers that ended up in our net," Calgary coach Bob Hartley said. "This league, it's not a feel-good league. Moral victories do not exist, you need to put points on the board."
The Avalanche scored first when O'Reilly one-timed a pass from P.A. Parenteau only 5:31 into the game. It was O'Reilly's sixth of the season and extended his goal streak to three games.
Avalanche D Ryan Wilson (back) was scratched from the lineup. Nick Holden played in his place against Calgary. Wilson is expected to miss at least two weeks. ... The Flames acquired D Ladislav Smid and goalie prospect Olivier Roy from Edmonton for center Roman Horak and goalie prospect Laurent Brossoit on Friday. Smid is expected to join the team in Calgary on Saturday while Roy will report to Anchorage of the ECHL. ... Duchene missed Thursday's practice with a bruise foot suffered in Wednesday's loss to Nashville.