Chicago (11-6-4) swept two games here after winning 6-5 in a shootout Tuesday.
"It shows we can win in different ways," Blackhawks coach Jeremy Colliton said. "Obviously, you love to score goals, but sometimes you can't control that.
"But how we defend and our commitment to the details and the work ethic away from the puck, that that we can control, so obviously as a coach you feel better about tonight's performance as far as that. We were really solid away from the puck."
Kane gathered the puck at the attacking blue line and skated to the right circle before using a snap shot for his third goal in as many games. He needs one goal to become the 100th NHL player to score 400.
"It was obviously a pretty tight game, both teams were grinding it out, trying to play tight," he said. "It was nice to get a break and be able to capitalize on it."
Kane has 13 points (four goals, nine assists) in six games against Columbus this season and 68 points (23 goals, 45 assists) in 52 career games.
"He's a tough player to stop," Blue Jackets defenseman Zach Werenski said. "He has so many ways to score whether it's his backhand shot, making a move."
Carl Soderberg scored into an empty net at 19:10 for the 2-0 final. He has a three-game goal streak after scoring once in his first 13 games with Chicago.
The Blue Jackets led in first-period shots (8-3) and attempts (18-6).
Patrik Laine hit the post at 1:36 and at 15:13 during a power play. Subban stacked his pads to stop Seth Jones at the near post at 7:37 and took a snap shot by Cam Atkinson off his upper body at 11:21.
At 15:16 of the second, Subban got help when a point-blank shot by Eric Robinson hit the post.
"I feel like I've never been good at getting shutouts in every league I've been, so I cherish them when I get them," Subban said. "But I think it's the result of our team play. It felt like a playoff game, and usually those are really tight."
The Blackhawks took more shots on goal (12-3) and attempts (25-12) in the second period.
Subban saved an Oliver Bjorkstrand shot and Kevin Stenlund's rebound try six minutes into the third period during a Columbus power play.
"We don't find a way to score and they do. One shot beats us," Blue Jackets coach John Tortorella said. "We play a good first period, they play a good second period, and it comes down to the third period. They score a goal and we don't."
NOTE: Subban made 20 saves in a 5-0 win against the Winnipeg Jets on March 21, 2019 while with Vegas.
