With the game tied, Antti Laaksonen took a shot from the slot that was kicked out by goaltender Marty Turco to Roest in the right faceoff circle. Roest wristed the puck just out of the reach of Turco's glove to put the Wild ahead.
Laaksonen, who had three assists, teamed with Roest to set up Pascal Dupuis' empty-netter that sealed the win with 10.5 seconds left.
Minnesota recorded just its third win in 11 games (3-6-1-1) but improved to 10-17-3-2 on the road.
The loss also ended Turco's personal four-game winning streak.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys