Jamie Benn had his 100th career goal and three assists for Dallas, which broke open a 2-1 lead with four second-period goals and ended Toronto's six-game winning streak.
Cody Eakin added a goal and an assist, and Alex Goligowski, Sergei Gonchar and Tyler Seguin each had two assists for the Stars, who won their second game in a row since ending a 1-8-1 slide. Kari Lehtonen made 24 saves.
Nikolai Kulemin had the lone goal for Toronto.
After Nichushkin's first goal, Toronto coach Randy Carlyle replaced Jonathan Bernier with James Reimer, who allowed the final four goals, including one on a power play by Shawn Horcoff and one short-handed by Rich Peverley.
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