Benn racked up his fourth straight multi-point game for Dallas when he scored on the rebound of an Adam Burish shot 7 minutes into the final frame, putting the Stars ahead to stay at 2-1.
He also notched the equalizer late in the second period, one-timing a Trevor Daly pass from behind the net to produce a 1-1 tie.
Richard Bachman turned aside 25-of-26 shots to collect the win.
Taylor Hall got the only goal for the Oilers, who fell to 0-10-1 in their last 11 visits to Dallas.
Nikolai Khabibulin made 30 saves for Edmonton.
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