The goaltenders took center stage at American Airlines Center on a night when the Stars honored 2011 Hall of Fame inductee Ed Belfour, who led Dallas to its only Stanley Cup in 1999. But after Kari Lehtonen of the Stars and Niklas Backstrom of the Wild were brilliant through 65 minutes, Loui Eriksson and Benn scored on both attempts for the Stars, sandwiched around a successful try by Minnesota's Matt Cullen.
Lehtonen then closed out the game by denying Jared Spurgeon's wrister.
Lehtonen finished with 33 saves through 65 minutes. Backstrom stopped 25 of the 26 shots he faced.
Dallas (27-22-2) opened the scoring at 15:12 of the second period when Mike Ribeiro scored a power-play goal. Kyle Brodziak tied it 5:18 into the third.
Belfour, who played for the Stars from 1997-2002, was honored in a pregame ceremony where the capacity crowd chanted his name in appreciation for his stellar 16-year NHL career,
For the most part, things were relatively quiet in the first 20 minutes. Dallas' Michael Ryder had the best chances, but he rang the crossbar on a wrister from the high slot and was denied by Backstrom on a breakaway.
However, after the Wild (25-19-8) had been on the power play three times -- once in the first period and two more in the second -- Dallas finally got an opportunity with the man advantage when Cullen was whistled for slashing at 13:53 of the second.
Dallas converted when Ribeiro knocked home a rebound after Alex Goligoski's slapper caromed off the end boards and landed right at his feet.
Minnesota tied the game when Nick Johnson intercepted a backpass by Dallas' Jake Dowell and quickly fed Brodziak, who skated across the front of the net and flipped a wrister over Lehtonen.
With 1:07 remaining in regulation, Dallas defenseman Sheldon Souray put the Wild on the power play by hooking Brodziak in the Stars' zone. However, Minnesota was able to muster few chances of note and the game headed to overtime. Lehtonen came up huge with a glove save to deny Dany Heatley’s 40-foot slapper 56 seconds into the extra period.
At 4:04 in overtime, Dallas got its second power play of the night when Cal Clutterbuck was called for tripping after he and Ribeiro got entangled in the corner. Wild defenseman Darroll Powe made a goal-saving play with 22 seconds left when he blocked a shot by Goligoski.
The Wild conclude their three-game road trip on Tuesday night in Columbus while Dallas will host Phoenix on Tuesday.