"When you've lost three straight and you're kind of reeling a little bit, you're not necessarily going to come out and blow the doors off a team," said Jets captain Blake Wheeler, who scored the tiebreaking goal late in the third period. "These guys are fighting for a playoff spot. We did a good job of staying patient with that game, kind of doing all of the things that we preached before the game, and we got rewarded."
Andrew Copp and Mark Scheifele scored, and Connor Hellebuyck made 35 saves for Winnipeg (35-18-3).
WATCH: [All Jets vs. Sabres highlights]
Jack Eichel scored, and Carter Hutton made 26 saves for Buffalo (27-21-7) in his first start since Feb. 1.
The Sabres, who defeated the Detroit Red Wings 3-1 here on Saturday, failed for the eighth straight time to win consecutive games (0-7-1) and have not won two in a row since Dec. 11 and 13. They are 4-7-1 in their past 12.
"It stinks because of the position we're in," Buffalo coach Phil Housley said. "We need points. It was tough because we win a game [Saturday] and I thought in the past our effort, or just the way we were playing, wasn't indicative of tonight. We came and we charged. It was a good, solid game by us."
Copp scored shorthanded on a breakaway to give Winnipeg a 1-0 lead at 3:01 of the second period. Buffalo defenseman Rasmus Dahlin couldn't keep the puck in at the blue line, and Copp scored the Jets' seventh shorthanded goal of the season.