Left wing Sean Avery recorded the second four-point game in his career with one goal and three assists.
New York, which gave Dallas a 1-0 lead on Brad Richards' 12th goal this season at 2:17 of the first period, won for the third time in four contests and finished a three-game homestand with a 2-0-1 mark.
Dallas also got a goal from Jere Lehtinen at 2:07 of the second.
Net-minder Marty Turco was beaten four times on 24 shots for the Stars, who have lost their last three contests and six straight road games.
Avery's first-period score was the game's lone power-play goal on 12 combined man-advantage chances.