"It's a credit to the guys," coach Todd Richards said after the Blue Jackets improved to 16-16-3 after a horrific 6-15-2 start, when they were without as many as nine top players. "Where we were a month and a half ago, that was a big hole. To get back to .500 is a good spot considering where we were. But we can't be satisfied with it."
Columbus scored a power-play goal at 5:57 of the third with the score tied at 1. Cycling the puck, Connauton slid a pass to David Savard at the top of the left circle. His hard one-timer beat goalie Darcy Kuemper stick side inside the near post.
Ryan Johansen added an empty-netter for his first goal in 12 games.
"We made our mistakes and Bob made some big saves," said Johansen. "It wasn't the prettiest win, but we'll take it."
Brandon Dubinsky had two assists for Columbus, which went 10-1-1 in December. It was the third time in franchise history that the Blue Jackets won at least 10 games in a month.
"Hockey's a game where when things are going well, (they) sort of (come) in bunches," said Connauton, a waiver pickup from Dallas on Nov. 18 who has been an important part of the club's turnaround. "We're just on one of those hot streaks right now and we just have to keep working on it and the good things will keep happening."
Zach Parise scored a power-play goal for the Wild, who've had 11 of their last 14 games decided by one goal.
The Wild, near the bottom of the league on the power play, had two chances with a man advantage in the opening period and scored on the second.
With James Wisniewski off for holding, Thomas Vanek carried the puck from behind the Columbus goal cage and fed Mikko Koivu in the right circle for a quick pass to the right doorstep for Parise's one-timer that beat Bobrovsky inside the near post. It was Parise's 14th goal of the season.
Bobrovsky had earlier stymied Koivu on a weakside one-timer.
Johansen had a prime chance late in the first but Kuemper deflected the point-blank shot with his shoulder.
The Blue Jackets evened things on a relatively innocent play with 46 seconds left in the second period.
After a scrum in front of the net, the puck ended up at the short boards on the left wing and Kuemper ended up without his stick. Connauton fired a low shot that sliced past two defenders and eluded Kuemper.
"I dropped my stick on the save before and the puck got shot into the corner," said Kuemper, who had 23 saves. "It shot right out to a guy for a one-timer."
"We should have gone into the third period up 1-0," said Parise. "It's tough when you give up one in the last minute of a period. It gets them excited and gets the crowd excited."
The Wild haven't won a second straight game since Nov. 20.
"We can't get on a roll," said coach Mike Yeo. "It's disappointing. That was a game that was there for us. But we didn't dig in deep enough to get it."
NOTES: During pregame warmups, Columbus announced it had extended the contract of left wing Nick Foligno through the 2020-21 season for a reported $33 million. ... Foligno was playing in his 500th career NHL game. ... It was the Wild's first road game on New Year's Eve in eight years. ... The Blue Jackets placed RW Cam Atkinson on the injured list on Tuesday (shoulder). He's expected to miss a week or two. ... The Wild reassigned G John Curry to Iowa (AHL) earlier in the day and activated starting G Niklas Backstrom, who had missed the last three games with an illness. ... Minnesota came in having lost 86 man games to injury; Columbus had lost 223.