Evander Kane led the way, scoring two power-play goals in the Jets' 4-2 win on Tuesday night.
"A lot of battles, especially in the third period," said Kane, who has four goals this season. "They got on us pretty good and controlled a seven-minute block, and we were able to hold on."
Winnipeg coach Paul Maurice agreed it wasn't always pretty, but he was happy with what he saw, especially from Hutchinson, who made 32 saves to improve to 4-1-1. He just meets the minimum games played to lead the NHL with a 1.50 goals-against average. He also has a .947-best save percentage.
"I liked out goaltender an awful lot," he said.
Bryan Little and Andrew Ladd both had a goal and an assist, and Blake Wheeler and Jacob Trouba added two assists apiece for Winnipeg, which snapped a two-game losing streak.
"We can get a little bit of that positive feeling going," Maurice said.
Jordan Leopold and Ryan Johansen scored for the banged-up Blue Jackets, who are on a franchise-record pace for games lost to injuries. Columbus, which entered tied for the fewest points in the NHL, have lost four in a row and 13 of 15.
"We had chances," Blue Jackets coach Todd Richards said. "Had a few posts. But posts don't count as goals. The big thing for me is that for two periods it looked like we played a tentative game. The third period we came out and played."
Kane gave Winnipeg a 2-1 lead when he tapped in a perfect centring pass from Dustin Byfuglien with 3:35 left in the second period to end the Jets' seven-game power-play drought.
"It's nice to finally get one on the power play, and hopefully that can start a trend," Kane said.
Just 31 seconds later, during a delayed penalty call when Wheeler was sent sliding into Columbus goalie Sergei Bobrovsky, Ladd scored his eighth goal as Bobrovsky had trouble squaring up to the shot with Wheeler still in the crease.
Johansen pulled the Blue Jackets within 3-2 at 9:47 of the third with his eighth. He curled around from behind the net and flicked in a backhander.
Brian Gibbons nearly tied it on a setup from Artem Anisimov on a 2-on-1 rush. The rebound caromed off the end boards to Anisimov, who couldn't jam in the bouncing puck.
Off another long pass and break, Cam Atkinson hit the right post with just over two minutes left.
"We were able to squeak it out and get the win," Kane said.
Hutchinson was at his best early in the third period, stopping Jack Jackson on a backdoor shot, and Nick Foligno from the slot.
"I'm feeling really good about where my game is right now," Hutchinson said. "I feel I'm reading the play well. I'm able to read those seam passes and know where players are on the ice."
Kane scored his fourth on the power play into an empty net to make it 4-2 at 19:42.
Winnipeg just missed tying the franchise record for fastest goal to start a game by one second.
The Jets won the opening faceoff, connected on a series of passes without Columbus touching the puck, and sent Little in alone. He deked Bobrovsky for his seventh goal at 9 seconds.
The recently acquired Leopold tied it on the power play at 3:42, snapping in a shot from the left circle for his first goal.
NOTES: The Jets' record for fastest goal is 8 seconds, done three times, most recently by Ladd on Feb. 28, 2013. ... Columbus D James Wisniewski, who earned his 250th career point with an assist, and Dalton Prout played in their 500th and 100th games, respectively. ... Columbus had won seven of the previous eight meetings, dating to the 2007-2008 season.