Bobrovsky stopped all 10 Sharks shots in the second period as the Blue Jackets used goals from James Wisniewski and Ryan Johansen to forge a three-goal advantage.
Marian Gaborik added a goal and an assist and Matt Calvert also found the net for Columbus, which came into the contest four points out of the eighth and final Western Conference playoff spot.
Antti Niemi yielded four goals on 26 shots before being pulled in the third period for San Jose, which fell to 6-11-2 on the road.
The Sharks held the No. 5 seed in the West.