The Blue Jackets scored four straight goals in the second period and Curtis McElhinney made 28 saves as Columbus (21-20-4) won its third straight game.
Ondrej Pavelec faced 26 shots for Winnipeg (19-23-5), who were booed at the end of the game.
The Blue Jackets' second-period barrage included four goals in the first nine minutes and seven seconds, starting with Letestu's short-handed goal 36 seconds into the period.
O'Dell scored his goal at 4:32 of the first period during a goal-mouth scramble when he banged in the puck with a backhand while McElhinney was out near the edge of the crease.
It was one of a number of roster changes for Winnipeg.
O'Dell's goal came a minute after the Jets had a goal called off after a review because Setoguchi had lifted his stick high after Mark Stuart fired a shot from the point.
Columbus regrouped during intermission and came out firing in the second and capitalizing on Winnipeg's errors.
Just nine seconds after Blue Jackets centre Brandon Dubinsky was called for holding 27 seconds into the period, MacKenzie and Letestu went on a two-on-one and Letestu deked and put a backhand shot past Pavelec.
Columbus made it 2-1 at 4:15 when Atkinson took a nice pass from Wisniewski as he was skating fast to the side of the net. He fired the puck high over Pavelec, who was stretched out on the ice.
Foligno opened the lead to 3-1 when he was all alone in front of Winnipeg's net as the Jets players were along the boards or behind the net.
Ryan Johansen was behind the net and sent a pass to Foligno, who easily beat Pavelec at 8:26.
Jenner then made it 4-1 just 41 seconds later with a low penalty shot on Pavelec's stick side after Jets defenceman Adam Pardy had hooked him on a breakaway.
Winnipeg finally stopped the bleeding after Little stole the puck in the neutral zone and made a pass to Enstrom, who beat McElhinney at 11:55 to close the gap 4-2.
The Jets had actually outshot the Blue Jackets 19-18 through the first two periods.
Jenner scored his second goal off a rebound with two Jets players beside him at 4:08.
Little made it 5-3 with a power-play goal at 5:55, but another Pavelec rebound ended up on the stick of Letestu at 11:14 for his fourth goal of the season.
Notes - The last time the Jets lost at least four in a row was late last season from March 28 to April 4, when they went 0-5-0 over that stretch … Letestu's shorthanded goal was the sixth one allowed by the Jets this season.