The win snapped a two-game losing skid for the Sabres.
Winnipeg, who were attempting to clinch a Western Conference playoff berth, will have to wait until Tuesday to do so when they host the Washington Capitals.
J.J. Peterka, Rasmus Dahlin, Alex Tuch and Tyson Kozak also scored for the Sabres.
Jacob Bernard-Docker had a pair of assists.
James Reimer turned aside 34 shots for Buffalo, who moved to 28-35-6.
Nino Niederreiter, Colin Miller and Nikolaj Ehlers scored for the Jets.
Logan Stanley had a pair of assists.
Eric Comrie stopped 12 shots for Winnipeg, who dropped to 48-19-4.
Peterka got the Sabres on the board 9:15 into the contest when he took a feed from Jacob Bernard-Docker before moving off the boards into the slot and before beating Comrie glove side with a hard wrister to make it 1-0 Buffalo.
The goal was his third in the last three games.
Nino Niederreiter tied the game just over two minutes into the second on a power play when his shot was stopped by James Reimer before Sabres defenceman Beck Malenstyn knocked the disc into his own goal with his skate.
The goal was his 15th of the season.
Rasmus Dahlin scored late in the second period when he converted a Jacob Bernard-Docker cross ice feed, blasting a slap shot past Comrie at 18:46 of the second.
The goal was his 13th of the season.
With Mark Scheifele off for tripping Buffalo scored on the power play when Tyson Kozak slid a backhand shot past Comrie 7:13 into the third to make it 3-1 Sabres.
Buffalo's two-goal lead was short lived as Colin Miller took a Mark Scheifele feed at the blue line before moving in and parking a shot just under the crossbar just 22 seconds later to make it 3-2.
The goal was Miller's 3rd of the season.
Alex Tuch scored shorthanded 13:21 into the third after Ryan Mcleod sent him in alone.
The goal was his 27th of the season.
Nikolaj Ehlers scored with 3:28 left in the third when he streaked down the left wing boards and hammered a slap shot past Reimer to pull the Jets to within a goal.
The goal was his 23rd of the season.
Mcleod added an empty netter with 46 seconds left in regulation to seal the win for Buffalo.
SHOTS-BUFFALO 17 WINNIPEG 36
ATTENDANCE-15,225
