Bouchard grabbed a turnover by Pavel Datsyuk at the blue-line, then lifted a backhand shot over Osgood's glove, giving Minnesota its NHL-best 11th overtime win of the season.
Tied 1-1 with less than four minutes to play in regulation, the teams traded goals just 16 seconds apart. Kris Draper gave the Red Wings their first lead, lifting his own rebound over Manny Fernandez's left leg pad. After the ensuing faceoff, Wild forward Mark Parrish deflected Keith Carney's shot that was heading wide left past Osgood, tying the game at 2-2.
Fernandez had 29 saves in the win, while Osgood stopped 32 shots in his first overtime loss of the season.