Josh Doan and Zach Benson each had two assists, and Ukko-Pekka Luukkonen made 23 saves for the Sabres (11-11-4), who have won four of their past six games.
“It’s speed combined with puck support. The puck support was real good,” Buffalo coach Lindy Ruff said. “We had a lot of bump back to speed that was real evident that led to goals. It was a night where we were really connected.”
Kyle Connor scored for the Jets (13-12-0), who have lost five of six. Eric Comrie allowed three goals on 14 shots before he was replaced by Thomas Milic (15 saves) at the start of the second period.
The teams will play again in Winnipeg on Friday.
“It’s pretty disappointing, that effort after playing a pretty good game in Nashville (a 5-2 win on Saturday),” Jets coach Scott Arniel said. “Obviously, three minutes into the game you’re down 2-0. We gave up nine rush chances, they scored four goals off the rush. ... Kicked ourselves on that one. We gave up all those rush opportunities and they capitalized on it.”
Jason Zucker gave Buffalo a 1-0 lead on a power play at 2:46 of the first period. Norris sent a backdoor pass to Doan, whose redirection at the edge of the crease was stopped by Comrie. However, the rebound trickled through Comrie's pads and landed in the crease, where Zucker jammed it in.
Bowen Byram scored 15 seconds later to make it 2-0. He took a cross-ice feed from Jack Quinn on a 3-on-1 rush and beat Comrie over his blocker from the left circle.
Norris pushed it to 3-0 at 14:04. He received a pass from Tage Thompson along the goal line, cut toward the net, and scored with a backhand that deflected in off the leg of Jets defenseman Dylan Samberg.
“To replace a guy like that is [almost] impossible,” Sabres forward Alex Tuch said. “He has such a high-end skill set, such a good skater. Just an unbelievable 200-foot centerman. His IQ is off the charts. He put it on full display tonight. He was unbelievable. When you miss a guy like that, it definitely hurts. It’s good to get him back.”