Joe Pavelski corralled the puck at the Wild blue line and fed it to Thornton, who scored on a shot from a sharp angle.
Thornton and Patrick Marleau scored less than a minute apart in the second period, erasing a 2-0 deficit.
Pavelski and Matt Irwin each notched two assists for the Sharks, who improved to 19-2-3 at home and reeled off a sixth straight win overall.
Antti Niemi stopped 20-of-22 shots to earn the victory.
Darcy Kuemper made 29 saves.
Notable deaths of 2014 [PHOTOS]