Andrew Cassels, playing his first game after missing 12 with a groin injury, had a goal and an assist while Jerome Iginla and Valeri Bure chipped in with two assists each as Calgary beat Vancouver for the first time in four meetings this season.
Flames goalie Fred Braithwaite's shutout bid was foiled 7:27 into third period, when Dave Scatchard scored a power-play goal after the Flames had built a 5-0 lead through two periods.
Stillman, who scored his 20th goal, is now tied for the team lead with 39 points two games after Calgary dealt Fleury to the Colorado Avalanche.
The win inched the Flames - 2-2-2 in their last six games - to within four points of the idle San Jose Sharks, who hold down the Western Conference's eighth and final playoff spots.
The Canucks, all but mathematically eliminated from post-season contention, lost their third straight and sixth in their last nine games. Vancouver, outscored 33-12 in its last nine outings, has now gone 4-11-3 since Marc Crawford took over as coach following Mike Keenan's dismissal in January.
After the Flames opened the scoring on Todd Simpson's goal from the blue line 1:50 into the game, they went up 2-0 while down two men.
Braithwaite set up a shorthanded goal, getting to the puck behind his net and clearing it up the left boards. Cassels got in behind Canuck defenseman Adrian Aucoin and chased down the pucjust inside the Vancouver zone. Cutting to the net alone, he switched the puck from his forehand to backhand and flipped it inside the far post with 6:39 left in the opening period.
The Flames, who entered the game with the NHL's worst penalty-killing percentage, had not scored while two men short this season.
Calgary sealed the victory with three second-period goals. Iginla set up Stillman for a tap-in power-play goal 7:08 into the period. Three minutes later, Jeff Shantz scored during a scramble in front, while Stillman made it 5-0 with another power-play goal with 5:45 left in the period.
Canucks goalie Garth Snow, who gave up five goals on the first 19 shots he faced, was pulled in favor of Kevin Weekes at the start of the third.
| Calgary's Todd Simpson almost hooks Alex Mogilny. (AP)|
Vancouver's injury woes deepened when Todd Bertuzzi, who had missed 31 games earlier this season with a fractured tibia, left the game a minute into the second period after he fell awkwardly, twisted his left knee and did not return. The Canucks opened the game already missing captain Mark Messier (knee sprain) and Dave Gagner (concussion).
Vancouver's Peter Zezel, meanwhile, played his first game after missing 25 with a fractured tibia.
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