Johansen handled a loose puck near center ice, skated in along the left side and fired a wrist shot that beat Thomas Greiss top-shelf on his glove side.
The Coyotes' Oliver Ekman-Larsson forced the extra session with his goal with 14.6 seconds remaining in regulation, firing a wrister from the point through traffic.
Johansen finished with one goal and an assist, while Blake Comeau, Boone Jenner and Mark Letestu also scored for the Blue Jackets, who moved into a tie with the Philadelphia Flyers for third place in the Metropolitan Division. Philadelphia is currently battling the Florida Panthers.
Sergei Bobrovsky allowed three goals on 32 shots in the win.
Martin Erat and Shane Doan both scored for the Coyotes, who moved into a tie with the Dallas Stars for the final playoff spot in the Western Conference with the point. The Stars are presently facing Nashville.