The Stars won for the fourth time in five games and they earned a point in their lone loss during that stretch.
Kevin Klein lifted Nashville into a 1-1 deadlock early in the second period, but it took Cole just 24 seconds to put Dallas back in front.
Cole then added a backhander with 5:56 to go in the middle stanza for a 3-1 lead and Ryan Garbutt tacked on a third-period goal for the Stars.
Kari Lehtonen made 33 saves in the victory. The four Dallas goals all came against Carter Hutton on 34 shots.
It was Nashville's fifth straight loss.