Sergei Bobrovsky made 35 saves for Columbus, including 19 in the second period.
The Sharks took a 1-0 lead at 9:22 on Boedker's first goal for San Jose since the former Arizona Coyotes forward signed as a free agent on July 1.
"It's nice to score and help the team get the lead," he said. "It was definitely a good one to get out of the way."
San Jose made it 2-0 on Ward's first goal of the season from a centering pass by Brent Burns at 14:54.
Werenski, the No. 8 pick in the 2015 NHL Draft, got his second point in his second NHL game at 3:44 of the third, 10 seconds into the Blue Jackets' second power play, to make it 2-1.
"In the third period we definitely took it to another level," Werenski said. "We have to do that the whole game, that's all."
Columbus had momentum but couldn't tie the game.
"There's no panic on the bench as ugly as it looked for a few minutes there," DeBoer said. "I thought our composure was still good, our confidence was still good."