Nico Sturm got the Wild within 3-2 at 14:09 when he redirected a shot by Brodin.
Minnesota (32-14-4) had lost four straight games to St. Louis, including the past two at home, 4-3 on Wednesday and 5-4 in overtime Thursday.
"We lost the two games, but for us, we realized that we could have won both games too," Sturm said. "It's not like we didn't have a chance to win those games. And even today, it just speaks to the group. … It speaks to the guys in the locker room to just once more get the job done.
"This is the kind of game that we need to play in two weeks when playoffs roll around."
The Wild are two points behind the Avalanche for second place in the West and six behind the Golden Knights for first. Colorado won 4-3 against the San Jose Sharks on Saturday.
St. Louis had won four games in a row.
"We played a solid two periods, got a 3-1 lead, just go close it out," Blues coach Craig Berube said. "All you have to do is manage the game. Advance the puck, make sure you get it in deep, get line changes, and just make hard plays."