In 1978, Edwards was named the top goalie for the Sabres. He played in 72 games and was selected to the NHL Second All-Star Team. Next season, the Sabres cut Edwards' games down because they were afraid of overusing him. Edwards shared his duties with goaltender Bob Sauve and Edwards finished with 26-18-9 record. In 1980, he and Sauve were awarded the Vezina Trophy for their performance. Edwards was also selected to the NHL Second All-Star Team and played in the All-Star Game. On February 24, 1982, Edwards was a part of history as he gave up Wayne Gretzky's 77th goal in a game vs. the Edmonton Oilers at Buffalo Memorial Auditorium. With that goal, Wayne Gretzky broke Phil Esposito's record of 76 goals.