With the Blue Jackets on a power-play, Rick Nash gained control along the right half-boards and fed a pass in the slot to Vermette, who stick-handled past a defender and back-handed it into the net, breaking a 1-1 tie with 4 1/2 minutes left in the frame.
David Savard added a goal and an assist, and Jeff Carter also found the net for the winners.
Columbus logged its second straight win with 28 saves from Curtis Sanford.
The Wild, meanwhile, lost for the third time in four contests.
Nate Prosser tallied and and Niklas Backstrom made 34 saves for Minnesota.