The Blue Jackets had picked up points in five of their past six games (4-1-1). The Jets won four of six games on a road swing only to return home and go 0-2-1 before heading to Columbus.
The Jets opened the scoring when Scheifele notched his fourth at the 13:59 mark of the second.
Finding his teammate off a nifty 2-on-1 pass below the hash, Kane, back in the lineup after missing six games with a lower-body injury, sent a pass to Scheifele that he lifted high into the top of the net.
Thanks to a double-minor for high sticking against Cam Atkinson, the Jets made it 2-0 at 2:28 of the third. A seemingly innocent one-timer from the blue line by Dustin Byfuglien was redirected by Little, who merely stuck out his stick. The puck ricocheted off it and also off the skate of Columbus defenceman David Savard's skate.
The goal was Little's team-high 14th of the season.
Columbus killed off the last 90 seconds of the penalty then got back in the game.
Umberger collected a pass from Matt Calvert behind the net and scored on the wraparound to cut the lead to 2-1 at 8:48.
Moments later, however, Savard got caught pinching in and it resulted in a 3-on-1 rush with Kane blistering a high shot to push the lead back to two goals at the 10:35 mark.
But once again the Blue Jackets countered, this time when Nick Foligno stole the puck in his offensive zone. Montoya stopped his shot, but Mark Letestu then fed Tyutin, who was crashing the net from the wing to make it 3-2 at the 11:39 mark.
The Blue Jackets pressed over the final 8 minutes, but never really got a good scoring opportunity.
The game pitted teams with almost identical records. But Columbus (14-15-4) came in only three points out of a playoff position in the East while tied for ninth place, while 12th-place Winnipeg (14-15-5) was 10 points out of eighth in the West.
Montoya got the start in goal after Ondrej Pavelec was pulled upon allowing five goals on 24 shots in the first two periods of a 6-4 loss to Dallas on Saturday night.
Mike McKenna, who had 29 saves, was starting his fourth consecutive game since backup Curtis McElhinney (lower body) was injured — in relief of last year's Vezina Trophy-winning goaltender Sergei Bobrovsky (groin strain).
There was little going on other than two fights in the opening period — until the final minute.
A wild scramble in the crease led to Calvert being checked into the cage just as the puck went past Montoya and into the net, possibly off the stick of Jets defenceman Jacob Trouba. But referee Tim Peel immediately waved off the goal while the crowd booed loudly.
Peel said Montoya did not have room to make a play on the puck.
The crowd booed louder each time the replay was shown on the centre ice monitors. The officials deliberated for 45 seconds, but Peel then announced that the call was non-reviewable.
Notes: Columbus was playing its sixth game without last year's Vezina Trophy-winning goaltender, Sergei Bobrovsky (groin strain). He'll probably miss another three weeks. ... The Jets were without RW Anthony Peluso, suspended for three games by the NHL for a hit on Saturday against Dallas' Alex Goligoski. ... The Blue Jackets should get RW Marian Gaborik (sprained knee) and D James Wisniewski (upper body injury) back this week. Around the holidays, they'll likely get Bobrovsky and prized free-agent signing RW Nathan Horton (shoulder surgery), who has yet to play a game in a Blue Jackets sweater. ... Columbus D Dalton Prout (upper body) and C Derek MacKenzie (lower body) were both hurt in the first period and did not return. ... Blue Jackets C Ryan Johansen extended his points streak to a career-best nine games (four goals, seven assists).
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