Jack Thompson scored his first NHL goal, and Fabian Zetterlund had two assists for the Sharks (4-8-2), who have won four of five. Macklin Celebrini had three shots in 17:06 of ice time in his return after missing the previous 12 games with a hip injury.
"It was tough to feel the rhythm," Celebrini said. "I mean, we're a month into the season, and it's the best league in the world, so, it's tough to jump right in and feel the speed right away, but I felt like I started to get a little bit better as a game went on."
Kirill Marchenko scored, and Merzlikins made 25 saves for the Blue Jackets (5-5-2), who have lost three in a row.
"We didn't play that rush very well," Columbus coach Dean Evason said. "We did a lot of the things we talked about. We kept the puck out of the net and had a ton of great looks, we just didn't score."
Carl Grundstrom appeared to have given the Sharks a 1-0 lead at 7:54 of the second period, but the goal was waved off after the Blue Jackets challenged the play for offside.
Thompson, who was playing in his 10th NHL game, did give San Jose a 1-0 lead at 18:49. He scored on a one-timer from the left circle off a cross-ice pass from Will Smith four seconds after a power play expired.
"[Thompson] has been good for us," Sharks coach Ryan Warsofsky said. "He had another good night tonight, and I am glad to see him get rewarded with the goal."