Aretmi Panarin streaked into the Winnipeg zone before feeding a wide open Zibanejad who golfed the disc past Connor Hellebuyck to give the Rangers their fifth straight win.
Artemi Panarin had a goal and two assists for New York.
Chris Kreider had the other Ranger goal.
Igor Shesterkin turned aside 27 shots for the Rangers, who moved to 7-2-0 on the season.
David Gustafsson and Nikolaj Ehlers scored for the Jets, who dropped their second straight game.
Cole Perfetti had a pair of assists for Winnipeg.
Connor Hellebuyck made 23 saves for the Jets, who dropped to 4-3-2.
Winnipeg started the game with a turnover when Jets captain Adam Lowry gave the puck away to Alexis Lafreniere 1:28 into the first, who skated in on a breakaway and shot the puck high and wide.
Kaapo Kakko took advantage of a giveaway in the neutral zone nearly scoring on a breakaway but Connor Hellebuyck turned him away.
Artemi Panarin opened the scoring at 18:24 when he redirected a Jacob Trouba slap pass on his backhand past an outstretched Hellebuyck to make it 1-0.
The goal was his 5th of the season.
David Gustafsson evened the contest at 19:32 after Cole Perfetti ragged the puck in from the neutral zone, drawing in the Ranger defence before dishing to Gustafsson who snapped the disc just under the crossbar to make it 1-1.
The goal was his 2nd of the season.
There was no scoring in the second period.
Nikolaj Ehlers scored just over five minutes into the third when he followed up on a thwarted 2-on-1 with Cole Perfetti as the puck ended up on his stick behind the Ranger net.
The Jet winger simply skated around the other side of the net and stuffed the disc past Shesterkin to give the Jets a 2-1 lead.
The goal was his 2nd of the season.
With Brendan Dillon off for boarding New York tied it up on the power play 13:12 into the third period when Chris Kreider tipped an Adam Fox shot from the point past Hellebuyck to make it 2-2.
The game went to overtime.
Winnipeg had a 1:19 power play in overtime but were unable to score.
Mika Zibanejad gave the Rangers the win with twenty six seconds left in overtime, one timing an Artemi Panarin feed past Hellebuyck to give New York the win.
New York returns home to face Carolina Thursday while Winnipeg visits Vegas.
SHOTS-NEW YORK 26 WINNIPEG 29
ATTENDANCE-11,898
NOTES-Jets winger Nikolaj Ehlers reached 400 career points with his third period tally.
