After Kyle Quincey opened the scoring for Colorado at 10:50 of the first period, Horak tied it 3 minutes later with a highlight-reel goal. He fended off the backcheck of Chuck Kobasew and then, while falling, tapped the puck out of the air and past goalie Jean-Sebastien Giguere.
"I just tried to put everything on net and when you put something on net, something good happens. And that's what happened today," Horak said.
Ryan Wilson also scored for Colorado, which had won six straight road games. The Avalanche were one short of the franchise record for consecutive wins away from home.
"If you look at the games we've played this season, whenever we've found ourselves down a bit in the third period, we've found a way to come back and at least give ourselves a shot -- and that says a lot about us," Colorado center Ryan O'Reilly said.
Horak had 78 points in 64 games with the WHL's Chilliwack Bruins last season and was the talk of training camp this year, with coach Brent Sutter impressed by the 20-year-old's two-way play. He was acquired from the New York Rangers in June for unsigned 2009 Flames first-round draft pick Tim Erixon.
But the regular season has been a struggle for the young Czech, who entered the night with no shots and one assist in five games, having been a healthy scratch twice.
"It's a way different game when the regular season begins," Horak said. "In the preseason, there are still young guys in the lineup and the older guys are just starting to get into it."
Horak's goal ended a scoreless stretch of 122 minutes, 55 seconds for the Flames, who scored four times in their previous three games. They were shut out 2-0 at home by Nashville on Saturday.
Horak also was in on Stempniak's goal 4:31 into the second period, which put the Flames ahead for good.
Giguere gave up a rebound and Avalanche defenseman Erik Johnson whiffed on his clearing attempt. Stempniak poked the loose puck into the net to give Calgary a 2-1 lead, with Horak getting the assist.
"He's a really intelligent player in all three zones," Sutter said. "For a young guy, he's done a really good job."
The Flames expanded their lead to 3-1 at 9:27 with a power-play goal. Anton Babchuk's shot bounced off Colorado defenseman Jan Hejda and went toward the net, where Bourque knocked it out of the air and past Giguere for his team-leading fourth goal.
Colorado dominated the third period, peppering Kiprusoff with 20 shots and eventually drawing within one goal at 15:29 when Wilson knocked in a rebound.
After being tested only five times in the first period, Kiprusoff made 30 saves over the final two, including 19 stops in the third.
"We still could play better," Bourque said. "We kind of let them back in the game there in the third, but Kipper played well and made some big saves. Credit to him for keeping us in there at the end."
The third-period domination by Colorado was a stark contrast to the first period, when Calgary controlled play and outshot the Avalanche 21-5.
"Our goaltender gave us a good chance in the first period. We were very fortunate to be 1-1," Colorado coach Joe Sacco said. "What we saw in the third period is more of a reflection on how we play."
Calgary led 11-1 in shots when Bourque took an offensive zone penalty that was promptly converted into a a power-play goal by the Avalanche at 10:50 of the first.
Paul Stastny's close-in chance rang off the post but caromed out the other side and onto the stick of Quincey, who put it in.
"There are games like that. It's part of goaltending," Kiprusoff said. "You have to just keep doing the same things. It doesn't matter whether it's 15 shots or five shots or one shot -- you just have to keep your eyes on the puck and keep it simple and not think about too much."
Calgary is 2-1-1 through the first four games of its season-long, six-game homestand. ... The Avalanche now head home, where they play 14 of their next 18 games. ... LW Curtis Glencross (lower body) did not play for Calgary. Inserted into the lineup as one of seven defensemen who dressed was Babchuk, who sat out five of the previous six games. ... Colorado was playing its first game within its division. Last season, the Avalanche were 7-16-1 against the Northwest. ... Calgary won five of the six meetings between the teams last season. ... Stastny's assist gave him 35 points (12 goals, 23 assists) against Calgary in 31 games, his most against any NHL team.