Norris had missed the previous 24 games after sustaining a lower-body injury in Buffalo’s season opener on Oct. 9.
Josh Doan and Zach Benson each had two assists, and Ukko-Pekka Luukkonen made 21 saves for the Sabres (11-11-4), who have won four of their past six games.
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.
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.
Connor cut it to 3-1 at 11:26 of the second period when he redirected Josh Morrissey’s one-timer from the point through Luukkonen’s five-hole.
Alex Tuch quickly responded for the Sabres to make it 4-1 at 12:49. Milic stopped his initial shot from the right circle, but Tuch collected his own rebound along the goal line and banked a sharp-angled shot in off the goalie’s left shoulder.
Norris extended the lead to 5-1 at 41 seconds of the third period. He skated into a touch-pass from Benson before slipping a backhand five-hole on a breakaway.
