Gorges, Evan Rodrigues and Rasmus Ristolainen all scored goals for the Sabres. Ristolainen's goal - a shot from the blue line that was mishandled by Bobrovsky - tied the game at 3-3 with 14:03 remaining in the third period.
It was a defensive-zone faceoff that led to Jenner's deciding goal later in the period. Ryan O'Reilly won the draw, but Cody Franson - thinking the puck would drift further than it did - handcuffed himself and fumbled the puck, leaving Jenner to pick it up alone near the net.
Jenner skated across the net, drawing Robin Lehner out toward the top of the crease, and tucked a backhand shot in behind the Sabres goaltender.
"I thought we did a lot of good things in that game," Franson said. "It's unfortunate that it comes down to that last goal, the way it was. It's a mishandled play on my part. It's not like I was trying to do something cute with it or something out of the ordinary. I was trying to keep it simple, just couldn't get a handle on it."
Bobrovsky entered the game riding a stretch of three straight shutouts, so it was atop the Sabres' list of priorities to pepper him with shots early and often. They ended any thoughts of a fourth shutout when Rodrigues scored a mere 2:50 into the contest.
The rookie stole the puck at the Columbus blue line, setting up a give-and-go with Nic Deslauriers that ended with Rodrigues roofing a far-side shot from the slot.