Josh Doan scored twice, and Josh Norris and Logan Stanley each had two assists for the Sabres (49-23-8), who have won three straight.
Buffalo is two points ahead of the second-place Montreal Canadiens, and four points ahead of the third-place Tampa Bay Lightning in the Atlantic Division. Both the Canadiens and the Lightning have played one fewer game than the Sabres.
Jet Greaves made 19 saves for the Blue Jackets (39-28-12), who have lost seven of their past eight games (1-6-1) and failed to gain ground in a tight Metropolitan Division race.
Peyton Krebs gave Buffalo a 1-0 lead at 13:41 of the first period. He skated down the right side before putting a snap shot under Greaves’ blocker from the right circle. The play started when Norris stripped Columbus defenseman Zach Werenski of the puck and found Krebs with a crossing pass entering the offensive zone.
Doan made it 2-0 when he stripped Blue Jackets forward Charlie Coyle of the puck at the Columbus blue line and beat Greaves under the glove from the top of the slot at 7:19 of the third period.
Jack Quinn pushed it to 3-0 at 13:21. He received a cross-ice pass from Stanley and roofed a wrist shot over Greaves, who couldn't get over in time to make the save. The goal marks Quinn's 20th of the season, the first time he has reached that milestone in his NHL career.
Just 25 seconds later, Doan scored his second of the night to extend the Sabres' lead to 4-0, receiving a pass across the crease from Zach Benson and slipping it past Greaves’ right pad at 13:46.
Rasmus Dahlin added an empty-net goal at 16:55 for the 5-0 final.