Brayden Schenn scored twice, and Brandon Saad had a goal and an assist for the Blues (20-18-3), who were coming off a 5-4 loss at the Montreal Canadiens on Saturday.
"I think we've done a good job this year on back to backs, and I don't think we have not been energized on back to backs," St. Louis coach Craig Berube said. "That's kind of what I was thinking.
"I felt like we were going to get a good effort tonight. We had some new guys in the lineup, a lot of young guys in the lineup. They're going to play hard, they're going to do their thing, and our veterans did a real good job of managing the game tonight, in my opinion. Managing the game, managing the puck."
Filip Gustavsson made 21 saves for the Wild (22-14-3), who have lost two straight, including 6-5 in overtime at the Buffalo Sabres on Saturday.
"I think the third period is more like how we used to play on nights where we win the game," Gustavsson said. "Just need to try and find a way to do it in the first and second period, too, and really force a goal. Maybe do an ugly goal or something. That's all we can do."
Saad gave the Blues a 1-0 lead at 8:17 of the first period, shooting into an open net on a power play after Jake Neighbours slid him a rebound in front.
It was Saad's fourth straight game with a goal.
"It's always nice to score goals and contribute to wins," Saad said. "My linemates are making great plays out there, so it's nice to see them go in."