It was the season opener for each team.
Knies, a forward, was acquired from the Toronto Maple Leafs on Monday as part of a six-player trade that sent forward Kirill Marchenko to Toronto.
Charlie Coyle had three assists, Zach Werenski had two assists, and Jet Greaves made 23 saves for the Blue Jackets.
Mattias Samulesson, Jack Quinn and Konsta Helenius scored, and Owen Power and Noah Ostlund each had two assists for the Sabres. Ukko-Pekka Luukkonen made 16 saves.
Knies gave the Blue Jackets a 2-1 lead at 17:58 of the first period with a power-play goal, scoring with a one-timer in the slot off a pass from Coyle.
Adam Fantilli scored at 18:44 to make it 3-1. He was a training camp holdout until signing a six-year, $82.5 million contract ($13.75 million average annual value) on Sept. 24 and did not play any preseason games.
Quinn pulled the Sabres to within 3-2 at 1:25 of the second period with a shot from the left circle.
Knies then extended the lead to 4-2 at 7:45 with a redirection after Columbus killed a penalty with Buffalo on the two-man advantage for two minutes. He is the first player to score multiple goals in his Blue Jackets debut and tied Artemi Panarin (three assists, Oct. 6, 2017) for the most points in a debut for Columbus.
Helenius cut it to 4-3 at 13:14 on a one-timer from low in the left circle.
Sean Monahan’s power-play goal at 14:21 of the third period made it 5-3, and Mathieu Olivier scored into an empty net 17:53 for the 6-3 final.
Samuelsson gave the Sabres a 1-0 lead at 7:21 of the first period with a snap shot from the high slot that deflected off the stick of Blue Jackets defenseman Denton Mateychuk during 4-on-4 play.
Cole Sillinger tied it 1-1 at 12:51, scoring from the left hash marks after taking a drop pass by Coyle.