Mark Giordano added a goal and an assist while Alex Tanguay, Blake Comeau and Olli Jokinen also scored for the Flames, who snapped a five-game losing streak and moved to within one point of the Western Conference's eighth and final playoff slot.
Miikka Kiprusoff turned aside 35 shots to collect the victory.
Jamie Benn scored twice while Mike Ribeiro and Philip Larsen scored a goal apiece for the Stars, who fell for the fourth time in six games but remain tied for first place in the Pacific Division and hold the third overall seed in the West.
Kari Lehtonen yielded five goals on 35 shots for Dallas.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
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