Jaden Schwartz scored for the sixth straight game and St. Louis hung on to beat Minnesota 2-1 on Tuesday night.
T.J. Oshie also had a goal for St. Louis, which is 5-0-2 in its past seven road games. The Blues are 8-1-2 in their last 11 overall.
Alexander Steen and David Backes, two of St. Louis' top scorers, were out with upper-body injuries, and the Blues then lost Chris Stewart in the first period when he was hit in the face by a shot from Jason Pominville.
"Our lineup is what it is right now and we've just got to find a way," Blues coach Ken Hitchcock said. "Nobody is feeling sorry for us. We've got to find ways to get points, and this is good."
Ryan Suter scored in the closing seconds for the Wild, who have lost a franchise-record six straight games in regulation, and are 5-12-1 in their past 18.
They have gone 10 straight games without a win in regulation, leading to speculation regarding coach Mike Yeo's job status.
"When things go bad, usually you have to hit the bottom before you can start going, and we're as close to the bottom as we can get," Suter said.
St. Louis, 13-0-1 against the Central Division, hadn't allowed a goal to the Wild for 212 minutes, 52 seconds before Suter scored with 8.3 seconds left in the game. The Blues are 5-0-2 in their last seven games against Minnesota, outscoring the Wild 22-8.
Brian Elliott (10-1-2), who made 24 saves, went 6-0-1 with a 1.67 goals-against average in December. His teammates blocked 24 shots.
"It just speaks of the commitment we have of winning games like this, when you're on the road and it's three tough ones in a row," Elliott said.
St. Louis beat Chicago 6-5 in a shootout at home on Saturday and won 3-2 in overtime at Dallas on Sunday.
Minnesota had allowed 24 goals in its previous five games -- 11 in its last two -- and much of Monday's practice surrounded defensive-zone coverage.
Yeo switched up the defensive pairings with Suter and Jared Spurgeon playing together, and Jonas Brodin teaming up with Marco Scandella. Suter and Brodin have been the team's top defensive pair for most of the season.
The switch seemed to work early as Minnesota limited the Blues to seven first-period shots, none that were difficult for goalie Josh Harding to handle.
"That's the only way in this league you can win, to play good defense for the full 60 minutes," captain Mikko Koivu said. "I thought we did that pretty good, but then two chances they capitalize, and that's pretty much the end of story."
Oshie gave the Blues a 1-0 lead at 6:49 of the second period.
Mikael Granlund turned the puck over as he tried to come out of the Minnesota end, and Schwartz snapped a quick backhanded pass to Oshie, who was behind two Wild defenders. Oshie, a Minnesota native, deked Harding and tucked the puck into the net.
"We expected a great effort from them, and I think we got that," Oshie said. "The first period they really took it to us, and we got saved by our goalie. After that, we started to get pucks behind them, and that led to our offense."
Schwartz made it 2-0 a little more than nine minutes later when his wrist shot from low in the right circle was partially stopped by Harding, but the puck trickled across the line. Schwartz has 11 points in eight games.
"I'm getting some bounces right now for sure," Schwartz said. "I'm just trying to do my job, and producing is part of it."
Minnesota, which has the second-fewest goals per game in the NHL (2.19) and the fewest in the Western Conference, was on the power play for most of the period's final two minutes. The Wild failed to generate a shot and were loudly booed off the ice when the period expired.
The Wild had another power play early in the third, but Schwartz had the best scoring chance when he got behind two defenders and was stopped by Harding.
"It feels a little bit like Groundhog Day right now. The difference is that every game has been a different story," Yeo said. "We had a good start. Our first was good against a team we knew was going to defend hard and play well, and then unfortunately we broke."
St. Louis is 12-1-5 in one-goal games this season. Minnesota 12-4-5. ... Blues D Kevin Shattenkirk had a six-game point streak snapped. ... This is the eighth consecutive year and 10th time in team history the Wild played at home on New Year's Eve.