Jamie Benn and Radek Faksa had the markers for Dallas.
The Stars - who were coming off a four-game losing skid on the road - continued their dominance at home, improving to 11-3-1 at the American Airlines Centre.
"We weren't competitive enough," said head coach Bill Peters, cutting to the chase when asked about the loss.
Captain Mark Giordano also didn't mince words.
"We weren't sharp and it showed right from the start," he said. "I think they looked like the faster team but only because they were committed to putting pucks in and forechecking.
"For whatever reason, we were fighting it all night and we weren't making clean plays. Not to take anything away from them, they played a hard fought game but I don't think we were sharp enough, for sure."
It was an uncharacteristically slow start for the Flames, who put up four in the opening frame against the Blues.
David Rittich was forced to make some big saves early as the Stars poured it on in the first period, outshooting the Flames 11-3 before finally getting one past him on their 12th try of the frame.
After a rare Mikael Backlund turnover in the Flames zone, Jamie Seguin gathered up the puck behind the net and skated out front throwing it across the crease where it bounced off the skate of linemate Benn and into the cage.
Dallas finished the opening 20 with a 13-5 edge in shots.
The Stars picked up where they left off to begin the second, outshooting the Flames 6-0 as Rittich was busy early and often.
Just before the mid-point of the frame, Garnet Hathaway ran into Stars goalie Ben Bishop as the big 'tender played a puck behind the net, with the rugged forward being sent to the box for goalie interference.
Not long after Bishop left the game, replaced by Anton Khubobin.
TJ Brodie had the best chance to that point of the night for the visitors, finishing a nifty three-way passing play with a great shot that Khudobin was able to get a piece of and steer away.
With less than three minutes to go in the frame off a scramble in the Calgary zone, Faksa gathered the rebound of a Martin Hanzal shot and went forehand-backhand to tuck it around Rittich who tried to poke check but missed the puck.
Bishop was back in the pipes to start the final 20, as the Flames looked for another installment of the third-period heroics they've become known for this season - outscoring the opposition by 28 goals in the final frame.
However, despite a hard push that included outshooting Dallas 11-2 at one point they weren't able to find the back of the net.
Peters said that with a tilt against the league's top team next up - the Tampa Bay Lightning at home Thursday - they need to move on quickly.
"You know what, we'll take 2-1 on the trip and we'll look at it on the way home and come up with a plan for our next game."
