Arttu Ruotsalainen and Michael Mersch also scored goals for the Sabres. Goaltender Aaron Dell stopped 12 of 15 shots before giving way to Dustin Tokarski, who turned away all but one of the 17 shots he faced and was perfect on three shootout attempts.
Jack Quinn scored the lone goal in the shootout.
"I think we just played with heart in the third," Peterka said. "Everyone was working for everyone and everyone was supporting, everyone wanted us to get the puck deep, to get the pucks on the net and everyone was also cheering for each other. That was an awesome feeling."
Peterka was one of a handful of players making their NHL preseason debuts, along with Quinn, Weissbach, and defenseman Oskari Laaksonen. Granato hoped for the game to be an introduction to the intricacies of playing against NHL competition. His message during the game was less about winning that it was about simply maximizing their intensity.
That they found a way to win in the end was icing on the cake.
"Everything should be meaningful, but in perspective," Granato said. "… It's preseason, it's not regular season NHL level by any means. But it's like when you go play in the backyard against your friends. You want to win. So, we have to have that approach any night."
Mersch set the stage for the comeback early in the third period when he drove to the blue paint and punched in a pass from Ryan MacInnis.
The score remained 4-2 until Weissbach set up Peterka's one-time goal with 2:04 remaining. Weissbach pounced on a loose puck off an offensive-zone faceoff and made an immediate feed to Peterka, who dropped to one knee as he scored from the slot.