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.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Millions of Getty images now available for free via embed tool