Former Edmonton Oiler Erik Cole, former Calgary Flame Eric Nystrom and Loui Eriksson scored for Dallas in a span of five minutes in the opening period to give the Stars a 3-0 lead.
The Flames marched back in the second period with a pair of their own before Eriksson sealed the game for the Stars with a game winning goal with 8:30 left.
Another Dallas Star that had a great game Monday was Fort Saskatchewan native Ray Whitney, who had a pair of assists. He continues to get the job done at the age of 40 with his great passing ability.
With the win, Dallas leapfrogs over Edmonton in the Western Conference and are one point back of the San Jose Sharks, who lost 5-3 to Anaheim Monday.
The Flames meanwhile are in 14th place in the Western Conference and are four points back of San Jose. The Flames next play in Nashville on Thursday.