Jack Roslovic scored twice, and Elvis Merzlikins made 25 saves for the Blue Jackets (35-36-6), who have lost three straight.
Columbus played without defenseman Zach Werenski and forward Patrik Laine, who are each out with an upper-body injury.
"This whole road trip has been two goals we got down within the first period," Roslovic said. "We can't try to come back every night, it's just too difficult to do in this league. It's just about being mentally focused right from the first puck drop. I guess we just didn't have it this road trip."
Reedy gave the Sharks a 1-0 lead at 4:39 of the first period, scoring a power-play goal on a rebound in front after Noah Gregor's initial attempt was saved by Merzlikins.
"[Reedy is] a guy that works hard, he's trying to get better every day," Boughner said. "And the offensive upside that he has, I think for a team that struggles to score, you want to keep developing these guys to have a touch around the net. You saw that touch tonight."
Rudolfs Balcers made it 2-0 at 8:45. He scored through traffic near the right hash marks after receiving a turnaround pass from Thomas Bordeleau from below the goal line.
"I thought they were really good," Boughner said of the line of Balcers, Bordeleau and Gregor. "'Rudy' and Gregor, I said after last game, that's the best I've seen them play together on a line, and I think a lot of that credit has to [go] to Bordeleau (who was playing his second NHL game). Slowing the game down a little bit, giving him pucks with full speed and being able to distribute them through the middle of the ice. I really liked that line, and I think Bordeleau had another strong game."