Benn has three goals and two assists in his last five games after going without a point for the first four games in 2016.
Dallas’ Jason Spezza scored in the first period and assisted on Jyrki Jokipakka’s goal in the second. Antti Niemi, who made 23 saves, allowed goals by Teddy Purcell on the power play in the second period and Nail Yakupov with 3:03 remaining in the game.
Cam Talbot had 32 saves for Edmonton, which had scored eight goals in splitting the first two games of their three-game trip, but managed only 25 shots on goal against Dallas.
After returning from an 0-2-1 road trip, the Stars improved to 18-5-0 at home this season. Dallas (30-13-5) pulled within three points of first-place Chicago in the Central Division.
The Stars scored 1:23 into the game. Spezza took a pass from Johnny Oduya in the slot, skated to his left and backhanded the puck under Talbot off his stick.
In the second period, Dallas didn't have a shot on goal for nearly 5 minutes until Talbot stopped Antoine Roussel's slap shot from the left faceoff circle.
Dallas appeared to take a two-goal lead at 9:31 of the second when Jokipakka shot the puck under the crossbar. Edmonton coach Todd McLellan challenged the goal, and a video review showed that the Stars' Ales Hemsky was offside before Jokipakka crossed the blue line.
The lead did increase to 2-0 at 13:16, when Benn scored unassisted. His wrist shot from high in the slot went inside the right goal post past an inadvertent screen by Oilers defenceman Mark Fayne.
Edmonton cut the deficit to 2-1 at 17:04. Purcell sent one shot off the left goal post, but regained the puck in the high slot and put a wrist shot just inside that post. The Stars have allowed five goals in 10 opponents' power plays over the last four games, but killed two of three on Thursday.
Just 15 seconds after Purcell's goal, Jokipakka restored Dallas' two-goal lead when his shot from the left circle went in off Oilers defenceman Benoit Pouliot's stick.
NOTES: Spezza has four goals in three games against Edmonton this season, including his first hat trick with the Stars on Oct. 13. He has 22 points (7 goals, 15 assists) in 20 career games vs. the Oilers. ... Dallas has won 10 of its last 12 home games - but the Stars are 0-5-3 in their last eight on the road. ... The Stars are 13-1-2 in their last 16 home games against the Oilers. ... Talbot has allowed only 19 goals in his last 11 games. ... Edmonton's penalty killers have an 89 per cent success rate (25 for 28) in the last 10 games. In Dallas' 11 most recent games, the Stars are at 11 per cent (3 for 28) on their power plays.