Martin Havlak forced overtime on a power-play goal with 57.6 seconds to go, jamming the puck past Jaroslav Halak from the side of the net. Andrew Brunette had a goal and assisted on the tying goal after the Blues were whistled for too many men on the ice.
David Backes had two goals for the Blues, and Andy McDonald added a goal and an assist. But St. Louis blew four one-goal leads, two of them within a minute, against a team ahead of them on the outskirts of the Western Conference playoff race.
Minnesota is 8-2 in its last 10 games, but had allowed only 13 goals in the previous nine. This was the first of a back-to-back, home-and-home series against St. Louis, with the teams meeting again Saturday night at Minnesota.
Pierre-Marc Bouchard, Mikko Koivu and Brent Burns also scored in the shootout, while T.J. Oshie, Brad Boyes and Alex Steen scored for the Blues. Madden scored on a backhander, and Jose Theodore stopped Vladimir Sobotka to decide it.
Backes leads St. Louis with a career-best 20 goals, four of them in the last three games. The Blues' top line of Backes, McDonald and Brad Boyes has 13 points in the last four games.
Clutterbuck leads the Wild with 16 goals, and answered Backes' score on a 2-on-1 break at 19 seconds of the third period only 22 seconds later to tie it at 3.
Notes: Blues D Carlo Colaiacovo wore a helmet with full cage in his first game back from a seven-game absence after taking a puck to the eye. ... McDonald has four points in four games back from a concussion that sidelined him for 24 games. ... The Wild are 16-9-3 on the road, among the best in the NHL.