John Mitchell and P.A. Parenteau each added two goals and an assist for the Avalanche (3-4), which snapped a three-game losing streak. Matt Duchene and Jamie McGinn both chipped in with a pair of assists.
Jiri Hudler had two goals and an assist in a losing cause for the Flames (1-3-1), who hadn't played since Saturday's 4-3 home win over Edmonton. Alex Tanguay had the other goal for the Flames, while Matt Stajan added two assists.
In his first start of the season for the Avalanche, Jean-Sebastien Giguere stopped 25-of-28 shots to pick up the win. Miikka Kiprusoff made 16 saves at the other end to take the loss.
Tied 3-3 in the third period and with Calgary defenceman Mark Giordano in the penalty box for tripping, Stastny scored his first of the season on an unassisted wraparound with 2:40 left in regulation.
He added his second of the 89 seconds later, before Parenteau scored into an empty net.
Hudler opened the scoring at 7:23 of the first period with his first of the season and first as a member of the Flames. Hudler set up the initial scoring chance when he feathered a pass into the slot that Stajan one-timed on net. Hudler the pounced on the rebound and swatted the puck past Giguere.
Tim Jackman nearly put the Flames up by a pair during a hard-working shift later in the first period. After being denied by Giguere on his first attempt, Jackman then tipped a shot off the post that trickled wide.
With just 47 seconds left in the first period, Mitchell intercepted a clearing attempt by Chris Butler before skating towards the slot and snapping a shot past Kiprusoff to tie the game.
The Flames then went up 2-1 early in the second period when Hudler finished off a nice three-way passing play with Stajan and Roman Cervenka. For Cervenka, it was his first NHL point after signing a free-agent deal with the Flames in the off-season.
After Parenteau backhanded a shot through Kiprusoff’s legs, Mitchell put the Avs up 3-2 when he converted a feed from Chuck Kobasew at 16:58 for his second of the game.
But with just 18 seconds left in the period, Tanguay wired a touch pass from Hudler past Giguere to tie the game at 3-3 heading to the third.
Notes: After finishing off a season-long, four-game road trip, the Avs will play their next four games at home starting on Saturday against Edmonton. ... The Flames have played four of their first five games at home. After hosting the Chicago Blackhawks at the Scotiabank Saddledome on Saturday, Calgary will embark on a three-game road trip starting in Detroit against the Red Wings on Tuesday. ... Heading into the game, Calgary had beaten Colorado in four of the previous five games at the Saddledome.Suggest a correction