Wild superstar Marian Gaborik, playing in his 500th career game, had one goal and two assists for a three-point night that made him a key part of Minnesota's victory.
Gaborik started off the scoring for Minnesota in the first period with a tip-in from Andrew Brunette.
Minnesota added two more goals in the second period. Eric Belanger and Owen Nolan both scored on the power play four minutes apart. Gaborik assisted on both tallies.
Although Minnesota got the win, it would need some help from above to advance closer to a Western Conference playoff spot.
The victory by the Blues keeps Minnesota three points out of the playoffs and with only two games remaining, the Wild will have to run the table to clinch a spot.
Minnesota will host Nashville on Friday night and travel to Columbus on Saturday for its final two regular-season games.
St. Louis will host Columbus on Friday and then travel to Denver to take on the Avalanche.
Minnesota will be eliminated from playoff contention with one loss or a St. Louis win in the next two games.