Netminder Marty Turco turned aside 40 shots as the Stars defeated the Wild for the 12th straight time in Dallas. Minnesota last won there on March 21, 2003.
Benn's long blast past backup Minnesota goalie Wade Dubielewicz with just over 3 minutes to go in the game was the back-breaker, coming only 53 seconds after Andrew Brunette's tally had pulled the Wild to within 3-2.
Guillaume Latendresse got the other goal for Minnesota, which turned to journeyman Dubielewicz while starting netminder Niklas Backstrom sat out a fourth straight game and backup Josh Harding was tending to a hip injury.
Dubielewicz stopped made 14 of 18 shots in his first NHL game since March 13, 2009, for Columbus.