The Wild trailed 4-1 going into the final four minutes of regulation and scored three times.
Boos poured down from the seats for a team that has blown leads repeatedly this season. But Desharnais got the only shootout goal and Setoguchi lost the puck, then fell on the Wild's last attempt to give Montreal the win, ending a season-high five-game losing streak.
Desharnais, who had three points, added a goal with both teams a man short.
Kassian scored his first two
Montreal played the Wild for the first time since an 8-1 win in Minnesota last season sparked by Subban's hat trick.
A sellout of 21,273 was announced, but there were hundreds of empty seats on a snowy night for a Montreal squad that started the day in last place in the
It was an eventful game from the start as
A couple of minor penalties later, Subban scored on a two-man advantage with a point blast at 2:33.
Only 19 seconds later, Wild goalie Niklas Backstrom seemed to pull something in a leg or groin and left the game in favor of
Minnesota got one back as Alexei Emelin was felled by an uncalled cross-check that left Kassian open to poke in
White got another fighting major and a misconduct later in the period for throwing punches at Veilleux, who had slashed goalie
Pacioretty, on his off wing to the right of Harding, put in his 26th of the season midway in the second period.
Desharnais tapped in a rebound of Pacioretty's short in the third period for his third goal in as many games.
Kassian, back in the lineup after sitting out two games, skated to the net and banged in his own rebound with a backhander with 3:53 left.
Coach Randy Cunneyworth's starting lineup included