The shootout lasted 7 rounds before the speedy winger skated in and beat Laurent Brossoit with a wrister just inside the post.
The win was their fourth in a row and handed the Jets their first defeat in their last four games.
Kyle Connor scored the Jets lone goal on the night.
Laurent Brossoit made 31 stops for Winnipeg.
Jeff Skinner scored for the Sabres.
Carter Hutton turned aside 25 shots for Buffalo.
There was no scoring in the first period.
Kyle Connor opened the scoring 7:10 into the second period, converting a Patrik Laine feed, beating Buffalo goaltender Carter Hutton just under the crossbar to make it 1-0 Jets.
Laine got control of the puck in his own end before skating through the neutral zone and feeding Connor who scored his 9th of the season.
Jeff Skinner tied the contest on the power play 53 seconds into the third period, snatching up a loose puck off a Jack Eichel shot before whipping a backhand shot past Winnipeg goaltender Laurent Brossoit to make it 1-1.
The goal was his 14th of the season.
"Fortunately for me today I think it kind of bounced around on my stick off of a rebound and I was able to get it up," said Skinner.
The game went to overtime.
There was no scoring in overtime and the game went to a shootout.
Jets captain Blake Wheeler said despite the game's outcome they did well on their four-game homestand, taking 7 of a possible 8 points though his 11 game point scoring streak came to an end.
“It’s not perfect, but it’s pretty darn close," said Wheeler. "Some things we can definitely build upon. We’ll get on the road and try to build that part of our game as well.”
Sabres Head Coach Phil Housley said he liked his club's effort on the night.
"I just think we bent a little bit but we didn’t break. I think last year we maybe would have broke a little more and gave the game away. We hung in there. That’s what’s great about this group, that they stick with it. We make some adjustments in between periods and they follow through with those adjustments. But it’s great for them, they’ve shown the resiliency up to this point in the season."
Buffalo-Eichel (score), Reinhart (miss), Mittelstadt (miss), Thompson (miss), Pominville (score), Okposo (miss), Sheary (score)
Winnipeg-Scheifele (miss), Laine (score), Wheeler (miss), Little (miss), Connor (score), Roslovic (miss), Perreault (miss)
SHOTS-BUFFALO 32 WINNIPEG 26