Valeri Nichushkin broke a 2-2 tie with a power-play goal in the second period and the Stars went on to record a fourth victory in six games.
Tyler Seguin had a goal and an assist while Cody Eakin and Shawn Horcoff also scored.
Kari Lehtonen stopped 30-of-32 shots for Dallas.
Jones, only the second goalie in NHL history to begin his career with eight straight wins, let in four goals on 23 shots.
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