Cole broke a 2-2 tie just 62 seconds into the final period and Dallas then came up with power-play goals from Jamie Benn and Cody Eakin to open a three-goal cushion.
Dallas scored three power-play goals in all while winning for the fourth time in six games.
The victory went to Kari Lehtonen, who made 30 saves. Minnesota had blasted Dallas 7-4 on Monday.
Jaromir Jagr was credited with an assist on the goal by Benn, giving him 1,000 for his career. He became the 12th NHL player to achieve that feat.
Minnesota had not lost on the road since March 5. Matt Hackett allowed five goals on 33 shots and the three third-period goals by the Stars came on just five attempts.
2014: The Year in Music [PHOTOS]