Jakub Voracek and Mike Commodore also scored for the Blue Jackets, who were 4-4-0 in the preseason and open the regular season against San Jose in Stockholm on Friday.
Robin Alvarez scored in the third period for for Malmo, the Swedish second-tier team.
Vermette opened the scoring 13:12 into the first period off an assist from Derick Brassard. Vermette made it 2-0 in the first minute of the second period — the first of three Columbus goals in the period. Voracek then made it 3-0 and Commodore put the Blue Jackets by four.