The Stars built a 3-0 lead early in the second period and then hung on for their fourth win in six games. Columbus missed a chance for what would have been its first three-game winning streak of the season, having recorded an NHL-low 15 victories.
After Nash scored with 7:48 to go in the middle period, neither side could produce a goal until Benn put one into an empty net with a second remaining in the contest.
Curtis Sanford stopped 31 shots for Columbus.
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