Brendan Gaunce beat Sabres goaltender Dustin Tokarski with a shot from low in the left faceoff circle to cut the Blue Jackets' deficit to one at 4:48 of the third period. Oliver Bjorkstrand tapped in a backdoor chance on the power play for the tying goal at 14:25.
Jakub Voracek scored the winning goal just 16 seconds into overtime, shooting across Tokarski's body from the right faceoff circle to culminate an end-to-end rush.
High-danger chances in the third period were 3-3, according to the analytics website Natural Stat Trick.
"They capitalized on two chances in 15 minutes and tied the game," coach Don Granato said afterward.
The Sabres were returning from a nine-day break for the All-Star Game. (The Blue Jackets returned from their break Tuesday in Washington.) Granato spoke prior to the game about recapturing the aggressive, fearless mentality that the Sabres had employed to start the season.
While chances against were limited, Granato did see examples of hesitation on Gaunce's tough-angle goal in the third period.
"The first goal of the period - and I know Tokarski would have loved to have that one back because it wasn't a great goal - we did back off," Granato said. "We had [two] opportunities to really keep a tight gap. We had numbers back. We had four back to their puck carrier.
"We backed [off]. And there's another indicator of that hesitation. That was a green light to be extremely aggressive. We had four back. We could have close that play out earlier before that shot."
Granato described Voracek's overtime winner in a similar fashion.
"We should've been up tighter on a gap," he said. "You wait for that speed to come against you, it's going to be tough, especially when it's a skilled player. Our mistake was not getting up ice and gapping up on it, which allowed that speed."