Bobrovsky started after backing up Joonas Korpisalo the previous three games. He ended a three-game losing streak and won for the first time since Oct. 18.
"He played outstanding," Foligno said. "That's what he's capable of doing. We knew it was just a matter of time for him to get going again. We were happy to be able to make some blocks for him. But man, when we needed him, he was huge, made some awesome saves."
Kevin Labanc scored, and Aaron Dell made 23 saves for the Sharks (6-4-3), whose six-game point streak (4-0-2) ended.
"We didn't pass well, we didn't play hard enough," Sharks forward Logan Couture said. "We didn't spend enough time in their end, we didn't forecheck, we turned too many pucks over. When you go down the list we did a lot of things wrong tonight and got what we deserved."
The Blue Jackets took a 2-1 lead on Jones' goal at 9:15 of the second period. Duclair's pass on a rush bounced off Jones' right skate in the low slot and into the net.
Foligno made it 3-1 when he took a stretch pass from Markus Nutivaara and scored with a backhand on a breakaway at 18:40.
"It just looked like the goalie didn't think I was going to have a chance on it," Foligno said. "He kind of relaxed and I just flipped it over his glove. It was nice to be able to put that one in for the team, especially at that moment. To be up 3-1 before the period ends is huge."
Anderson scored a shorthanded, empty-net goal at 18:59 for a 4-1 advantage.
"We probably played our best game away from the puck, easily," Columbus coach John Tortorella said. "Thirty blocked shots, 27 hits. I think we had the right attitude tonight and the right style of play."
Labanc gave San Jose a 1-0 lead at 11:50 of the first period, taking a pass from Couture and scoring on a slap shot from the left face-off circle. Couture extended his point streak to eight games (five goals, eight assists), tying his NHL career high. He also had an eight-game point streak from Jan. 21-Feb. 10, 2012.
"It was good to get the monkey off my back but we didn't get the two points," said Labanc, who ended a 10-game goal drought.
Columbus tied it 1-1 on Duclair's wraparound at 16:30. Ryan Murray sent a shot wide left, and the puck bounced off the boards to Duclair, who skated behind the net and scored before Dell could recover.
"I thought we played desperate tonight," Jones said. "I thought we were gritty. We were quick, we were physical. It was awesome to see late in the third when we were holding that lead, guys were diving, guys blocking shots, laying their body on the line."