Kari Lehtonen made 18 saves as Dallas won for the second time in its last 11 games. It was his second shutout of the season and No. 24 for his career.
Minnesota (27-20-5) dropped to 7-3 in 2014.
Cole's goal at 16:45 of the first gave Dallas a 2-0 lead. It extended the Stars' season-high streak to five consecutive games with at least one power-play goal.