Loui Eriksson scored for Dallas in the first round, but Matt Cullen got the Wild even in the second. Benn then beat Wild goaltender Niklas Backstrom with a wrist shot to give Dallas the advantage, and Kari Lehtonen denied Jared Spurgeon to gain an extra point for Dallas.
The Stars are 11-0-4 in their last 15 home games against the Wild, who haven't won in Dallas since a 3-2 overtime victory on March 21, 2003.
Kyle Brodziak scored and Backstrom stopped 25 shots for the Wild.
Mike Ribeiro notched a power-play goal and Lehtonen made 33 saves for the Stars.
Minnesota had won its previous two road games after going 11 games without an away victory.
The Wild went on the power play with 1:07 left in regulation when Sheldon Souray was whistled for hooking. The power play extended into the 5-minute overtime, but the Wild couldn't capitalize.
Dallas had a power play opportunity in the final 55 seconds of the extra session when Cal Clutterbuck was called for tripping, but the Stars were unable to generate many chances.
Ribeiro took advantage of Dallas' first power play of the night for the game's initial goal with 4:48 to go in the second period.
Teammate Alex Goligoski's shot from the point missed the net and bounced off the end boards. Minnesota's Nick Schultz attempted to clear, but the puck wound up on the stick of Ribeiro, who buried his 11th goal of the season from the slot.
Minnesota drew even at 1 at 5:18 of the final period with the help of a turnover by Dallas' Jake Dowell. Dowell's backhand pass up the middle of the ice was intercepted by Brodziak, who skated in alone and lifted a shot over a sprawling Lehtonen for his 15th of the season.
Brodziak has at least a point in each of his last six games.
NOTES: Former Stars G Ed Belfour was recognized before the game for his induction into the Hockey Hall of Fame Class of 2011. Ex-teammates Joe Nieuwendyk, Mike Modano, Brett Hull and Jere Lehtinen participated in the ceremony. All were members of the Stars' Stanley Cup championship in 1999. Fans chanted "Eddie-Eddie" as highlights of Belfour's career were shown on the video board. ... Stars RW Michael Ryder played his 600th NHL game. ... C Erik Christensen, acquired Friday in a trade with the New York Rangers, made his debut for the Wild, missing as Minnesota's leadoff man in the SO. ... Dallas LW Brenden Morrow (upper-body injury) missed his eighth game this season. The Stars' captain has been the subject of trade rumors. ... The Wild were without C Mikko Koivu (shoulder), D Clayton Stoner (lower-body), LW Pierre-Marc Bouchard (concussion), LW Guillaume Latendresse (concussion) and RW Jarod Palmer (concussion).