T.J. Oshie also had a goal for St. Louis, which is 5-0-2 in its past seven road games. The Blues are 8-1-2 in their last 11 games overall.
Ryan Suter scored in the closing seconds for the Wild, who have lost a franchise-record six straight games in regulation and are 5-12-1 in their past 18. They have gone 10 straight games without a win in regulation, leading to speculation regarding coach Mike Yeo's job status.
St. Louis, 13-0-1 against the Central Division, hadn't allowed a goal to the Wild for 212 minutes, 52 seconds until Suter scored with 8.3 seconds left in the game.
Brian Elliott (10-1-2), who made 24 saves, went 6-0-1 with a 1.67 goals-against average in December.