The game was tied 1-1 when rookie Chiasson took a pass from Ray Whitney and shot the puck into the upper right corner over Calgary goalie Karri Ramo at 11:11 of the second period.
At first, the shot was ruled no goal. But after a review showed that the puck reached the net before bouncing out, the score went to 4-1 within the next 1:01.
Just 18 seconds after Chiasson's second goal of the game and fifth this season, Benn's shot from the left circle went in for his second goal of the season.
Brenden Dillon then scored off a faceoff, assisted by Shawn Horcoff, at 12:12.
Goalie Kari Lehtonen returned after five games on injured reserve because of a leg injury.
Dallas had lost four of the five games while Lehtonen was out. Against Calgary, he made 28 saves.
Dallas dominated the early going, with the game's first four shots on goal. Two of those were by Chiasson.
Ramo stopped the first from in front of the goal, but Chiasson retrieved the puck and tapped it in for a 1-0 at 4:04 of the first period.
After that, Calgary took charge, outshooting Dallas 10-4 to end the period with a 10-8 advantage. The Stars still led 1-0.
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The Flames (4-4-2) tied the game 4:30 into the second period. Lee Stempniak skated along the right wing. Defenseman Trevor Daley stayed with a Flame across the ice and when center Cody Eakin skated from behind Stempniak, he shot the puck past Lehtonen.
Chiasson had a chance for a third goal late in the second period from the left circle, but Ramo deflected the puck wide of the net.
Benn scored again at 3:36 of the third period. A missed shot went off the back boards. Chiasson picked up the puck and slid it behind the goal to Benn. His wraparound shot beat Ramo.
The Stars outshot Calgary 15-9 in the second period and 11-10 in the third for a 34-29 advantage.
Dallas (4-5) twice in the third period failed to score on 5-on-3 advantages against a Flames penalty-killing unit that ranked last in the NHL.
NOTES: Dallas defenseman Kevin Connauton made his NHL debut. He was on the ice for the first goal, and was penalized for holding at 16:41 of the first period. ... Stars forward Ryan Garbutt served the first game of a five-game suspension for charging Anaheim's Dustin Penner. ... Calgary center Matt Stajan also returned from a leg injury that had kept him out since Oct. 3. He assisted on the Flames' goal. ... In his second NHL game, Calgary defenseman Christopher Breen drew a 5-minute penalty for fighting with Dallas' Lane MacDermid.
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