Rookie center Warren Peters pressured Fabian Brunnstrom into giving up the puck in his zone. Dustin Boyd kept the play onside and swept a pass to Nystrom as he broke to the net.
Nystrom moved in and fired a shot from 20 feet that squeezed in under the arm of goalie Marty Turco. Nystrom's fourth goal of the season was his first in 14 games.
Jamie Lundmark also scored for the Flames, who increased their Northwest Division lead over Vancouver to five points.
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Brendan Morrison scored the lone goal for Dallas, ninth in the Western Conference.