The 23-year-old forward, who was an undrafted free agent, was recalled from Wilkes-Barre/Scranton of the American Hockey League earlier in the day.
Ben Kindel also scored twice, and Arturs Silovs made 26 saves for the Penguins (29-15-12), who had lost two in a row but are 7-1-1 in their past nine games.
Jason Zucker and Tage Thompson scored for the Sabres (32-19-6), who have lost three of four following a five-game winning streak. Alex Lyon made 27 saves.
Zucker gave Buffalo a 1-0 lead at 1:46 of the first period. He took a pass from Ryan McLeod at the blue line to the top of the left circle and beat Silovs with a wrist shot to the far side.
Hayes tied it 1-1 at 9:18 when he beat Jacob Bryson to a loose puck for a short breakaway and snapped it past Lyon.
Hayes then gave the Penguins a 2-1 lead at 18:47. Anthony Mantha sent a no-look pass through his own legs from behind the net for Hayes low in the left circle, where he put a rising snap shot by Lyon glove side.
Kindel extended it to 3-1 at 7:44 of the second period, scoring bar down from the left circle on a 2-on-1.
Thompson scored on the power play to cut it to 3-2 at 1:55 of the third period when he lifted a wrist shot short side from the goal line over Silovs’ right shoulder.
Tommy Novak was in front to make it 4-2 at 15:33, putting the rebound of Egor Chinakhov’s point shot past Lyon’s glove.
Kindel scored an empty-net, short-handed goal at 19:46 for the 5-2 final.
