Peterka, who also had an assist, has four goals in his past three games.
Tage Thompson had a goal and an assist, and Ryan McLeod also scored for a third straight game for the Sabres (2-4-1). Ukko-Pekka Luukkonen made 35 saves.
Craig Smith scored his first two goals of the season for Chicago (2-3-1). Lukas Reichel had two assists, and Arvid Soderblom made 18 saves.
Thompson gave the Sabres a 1-0 lead at 8:39 of the first period. Peterka entered the offensive zone with the puck. Blackhawks defenseman Alex Vlasic attempted a poke check, but the puck went to Thompson, who put a wrist shot past Soderblom.
Beck Malenstyn’s goal off a double deflection made it 2-0 at 11:31. Connor Clifton’s turnaround shot from inside the blue line caromed off Chicago defenseman Wyatt Kaiser and Malenstyn.
Smith scored for the Blackhawks to make it 2-1 at 6:28 of the second period. Reichel made a cross-ice pass from the red line to Smith, who skated in and fired in a wrist shot from the top of the left face-off circle.
Reichel and Smith clicked again to tie the score 2-2 at 12:48. Reichel’s shot from the slot was stopped by Luukkonen, but the rebound went right to Smith, and he tapped it in.
Peterka restored Buffalo’s lead to 3-2, taking a feed from Thompson and putting a forehand shot into the open net from off the crease at 18:37.
McLeod scored into an empty net at 19:34 for the 4-2 final.
