Dallas goalie Kari Lehtonen made 26 saves and allowed only one goal for his 100th win with the Stars.
The Canucks (20-11-6) lost on the road for the second time in three nights, following a seven-game winning streak.
At 4:34 of the first period, Benn lifted a shot over Canucks goalie Roberto Luongo on assists from Seguin and Cole.
Peverley sent a pass across the goal mouth to Sceviour, who scored at 4:49 for his third goal in four games this season.
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