Wingels crashed the net and scored what turned out to be decisive goal 5:11 into the third period to give San Jose a 3-1 advantage.
The Sharks outshot the Blue Jackets 19-4 in the final period to secure their second victory in three games heading into a 20-day break during the Sochi Games.
Antti Niemi turned aside 19-of-21 shots to earn the win.
Ryan Johansen scored his 24th of the season and Boone Jenner added a third-period goal for Columbus, which dropped a second straight.
Sergei Bobrovsky made 44 saves.