The Sabres (21-15-4) had won 10 straight games three other times in their history, most recently from Nov. 8-27, 2018.
Zach Werenski and Damon Severson each had two assists, and Jet Greaves made 31 saves for the Blue Jackets (18-16-6), who have won four of five. Werenski, who on Friday was named to the United States roster for the Olympic Winter Games Milano Cortina 2026, returned after missing four games with a lower-body injury.
Josh Doan scored, and Ukko-Pekka Luukkonen made 29 saves for the Sabres, who had allowed two or fewer goals in their previous six games (nine goals).
Mateychuk put Columbus ahead 1-0 at 3:00 of the first period with a snap shot from above the right face-off circle following a drop pass by Boone Jenner.
Doan tied it 1-1 at 11:26. He was at the right post for a tap-in off a pass from Josh Norris after Owen Power intercepted a clearing pass by Mathieu Olivier.
Brendan Gaunce gave the Blue Jackets a 2-1 lead at 14:04 with a short-handed goal. Sabres forward Tage Thompon fell down at the offensive blue line, giving Gaunce a breakaway that he finished with a shot through the pads.
Dmitri Voronkov’s tip of Ivan Provorov’s shot made it 3-1 at 17:12, with the puck barely trickling across the line.
Olivier extended the lead to 4-1 at 8:04 of the second period. He took a flighted pass from Zachary Aston-Reese, skated to the net and snuck a backhanded shot through Luukkonen.
Cole Sillinger scored into an empty net at 11:46 of the third period for the 5-1 final. It was a 5-on-4 situation with each team serving a penalty.