Minnesota lost 6-5 at home against Colorado on Monday night, a game in which coach Jacques Lemaire was "shocked" at how bad his team played.
"I think we learned our lesson Monday that we're not going to get anything for free in this league. It was good to have a game today, so we could come out and show we are not that bad how we played Monday," Backstrom said.
That was especially true for the Minnesota goalie, who allowed six goals in two periods before being removed Monday.
Backstrom has won four of five against St. Louis, allowing six goals in those games.
He won 11 of his first 15 starts and had a 1.92 goals-against average, but was just 2-4-0 with a 3.57 GAA in his previous six starts.
"He's back the way he was," Lemaire said. "Everyone was open Monday and we couldn't stop the puck. Tonight, we were a lot sharper."
Backstrom's best save was a sprawling stop against B.J. Crombeen when he reached back and up with his stick to thwart a backhand attempt that was heading for the top corner during a first-period power play.
Belanger and his Minnesota teammates knew they were awful in their own end Monday.
"You don't want to see goalies get five or six goals scored on him. It was really important for us to get the shutout for him. He deserves it."
St. Louis was shut out for the third time this season. The Blues have lost three of their last four games.
"I think it's back to old school hockey where you tighten up defensively and wait for the other team to make a mistake, then capitalize on it," right wing David Backes said. "They definitely capitalized. We had a few chances where we don't bury the puck and Backstrom definitely made a few great saves tonight."
Belanger has three goals and three assists in his last five games, and Bouchard has three goals and three assists in his past three games after managing only a goal and an assist in his previous 15 games.
The goal came 4 minutes after Backstrom slid across the crease to stop Brad Boyes after a cross-ice feed from Patrik Berglund during a 2-on-1.
Brunette and Zidlicky scored power-play goals early in the third period for Minnesota. The Wild have 10 power-play goals in their last three games.
"We moved the puck around really well," Brunette said. "In this league, power-play goals are a big deal -- the difference between winning and losing games."
St. Louis coach Andy Murray said the Wild were simply more assertive in the final period. "When you play in your own zone you have a tendency to take some penalties and that's what we did. You've got to make the other team take some by playing in their zone and we weren't determined enough."
Miettinen was dragged down by Carlo Colaiacovo going in alone on an empty net in the final minute, and was awarded a goal.
Minnesota had a season-high 37 shots.
Zidlicky has scored 12 goals since Nov. 25, 2006, all but one on the power play. ... St. Louis forward T.J. Oshie, who has missed 13 games with a high ankle sprain but resumed skating last week, is on the trip. He is listed as day-to-day. ... Cal Clutterbuck returned to the Minnesota lineup. The rookie RW sat out the last two games after Lemaire suggested he'd slowed down a bit after being praised by his coach. ... Boyes scored both goals in a 2-1 win in Minnesota 11 days ago.
Copyright by STATS LLC and The Associated Press
Arena: Xcel Energy Center Location: Saint Paul, Minnesota
Referees: Paul Devorski, Greg Kimmerly Linesmen: Derek Amell, Scott Driscoll
Attendance: 18,568 (102.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Eric Belanger (7)
Assist: Pierre-Marc Bouchard
Andrew Brunette (9)
(Power Play) Assists: Marek Zidlicky, Marc-Andre Bergeron
Marek Zidlicky (4)
(Power Play) Assists: Marc-Andre Bergeron, Mikko Koivu
Antti Miettinen (7)
(Empty Net) Assist: Eric Belanger