Emil Bemstrom, Kirill Marchenko and Carson Meyer also scored for the Blue Jackets. Daniil Tarasov started in goal and made nine saves in 31:24 before being replaced by Jet Greaves, who stopped all 13 shots he faced in relief.
Chase Priskie scored, and Eric Comrie made 27 saves for the Sabres.
Bemstrom gave the Blue Jackets a 1-0 lead at 8:47 of the first period. Andrew Peeke, who signed a three-year, $8.25 million contract ($2.75 million average annual value) with Columbus earlier Wednesday, had the secondary assist on the play.
Marchenko made it 2-0 with a power-play goal at 13:29.
Priskie cut it to 2-1 at 3:49 of the second period, but Voracek restored the two-goal lead for Columbus at 7:58 of the third period.
Meyer scored a short-handed goal at 16:36 for the 4-1 final.
