Nino Niederreiter added a goal and an assist to help the Wild snap a nine-game losing streak against the Blues and win for the sixth time in seven games.
St. Louis dropped its fourth straight and also lost star T.J. Oshie after he was shouldered in the face by Wild enforcer Mike Rupp halfway through a chaotic second period. Rupp was ejected, Oshie dabbed blood from his mouth as he moved slowly back to the locker room after being down on the ice for 5 minutes.
Rupp was assessed a match penalty for intent to injure.
Curry, the fifth goalie Minnesota has started against St. Louis in five games, was called up to make his fifth NHL start. The Minnesota native had allowed 22 goals in his previous five games at AHL Iowa, but turned away four early power-play shots and had 17 saves in the first period to establish himself in his first NHL start since Jan. 11, 2010.
Minnesota led 1-0 after the first on Niederreiter's 14th goal and was controlling play during the first half of the second.
Then, Rupp, playing for the first time since Feb. 1, knocked Oshie out of the game, and Shattenkirk tied it with a 5-on-3 goal a few seconds later.
Brodziak and Schwartz traded short-handed goals before Matt Moulson buried his 23rd of the season at 17:30 to send the Wild into the second intermission with a 3-2 lead.
It took Brodziak only 58 seconds to extend Minnesota's lead to 4-2 in the third period with his eighth goal.
Blues goalie Ryan Miller, who had stopped only nine of 13 shots, didn't leave immediately after Brodziak's second goal, but skated back to the locker room and was replaced by Brian Elliott at 16:22 of the third.
After Brodziak's first goal, Blues center Steve Ott was given a 10-minute game misconduct penalty for inciting the opponent.
St. Louis entered the game second in the Western Conference, and there's a strong chance these teams could meet in the first round of the playoffs.
St. Louis had pushed the Wild around all season, but the momentum appears to shifting as both teams approach the postseason. In addition to beating the Blues, Minnesota has recently defeated Boston, Pittsburgh and Los Angeles.
NOTES: The Blues have been outscored 16-4 during their four-game slide. ... Wild D Christian Folin made his NHL debut and recorded an assist. ... Oshie hasn't scored a point since recording a hat trick against Minnesota on March 27.