On February 24, 1982, Edwards was a part of history as he gave up Wayne Gretzky's 77th goal of the 1981-82 NHL season in a game vs. the Edmonton Oilers at Buffalo Memorial Auditorium. Gretzky broke Phil Esposito's former single season record of 76 goals and finished the year with 92, which still stands as an NHL record.
Edwards played his junior hockey with the Ontario Hockey League's Kitchener Rangers, where he led the league in shutouts and goals against average in 1973-74, and was named to the league's All-Star team in 1973-74 and 1974-75. He was drafted by the Sabres in the fifth round of the 1975 NHL Draft (135th overall), and he began his professional career with the American Hockey League's Hershey Bears.
On February 13, 1977, Edwards played a role in perhaps the most unusual event in Sabres history. A day after Edwards reported to Buffalo from Hershey, Sabres general manager Punch Imlach ordered coach Floyd Smith to have Edwards replace expected starting goaltender Al Smith:
"I got to the locker room at about 5 p.m. for the game. We all went out on the ice and Al Smith took all of the warm-ups. Then I was sitting next to him in the locker room right before game time and said 'Good luck tonight.' He looked at me and said 'You don't know you're playing?'"
"That sort of ended the conversation right there. I was dumbfounded. So they play the anthem and when it ends Al hops off the bench, skates about five strides and says 'See you, Seymour' to [Sabres owner] Seymour Knox in the crowd. Then he skates off the ice. So it's my first game in the NHL and I was the only goalie in uniform.
Despite the incident, the Sabres defeated the Minnesota North Stars, 6-2.
Although Edwards enjoyed several successful seasons in Buffalo, he named the Sabres' 6-1 victory over the Soviet Red Army on January 3, 1980 as his greatest moment in a Buffalo uniform. Edwards was named the game's most valuable player.
"I have this belief that hockey is a North American game, and I still believe that today. The Soviets were great intimidators, and I remember Team Canada '72. Then I had the chance to personally go through that intimidation stuff on the ice. Because of it, I had a distinct dislike of the Soviets and wanted to do everything I could to beat them.
On June 9, 1982, the Sabres traded Edwards, Richie Dunn, Buffalo's second round choice in the 1982 NHL Draft, and Buffalo's first round choice in the 1983 NHL Draft to the Calgary Flames in return for Calgary's first and second round choices in the 1982 NHL Draft and first and second round choices in the 1983 NHL Draft.
"I cried like a baby. Honestly, I loved the community, I loved the team, and I loved my teammates. It takes a big piece out of you. But you have to get on with your life. I think every player should see two or three cities in his career.
On May 29, 1985, the Flames traded him to the Toronto Maple Leafs in return for Toronto's fourth round choice in the 1987 NHL Draft.
He retired after the 1986 playoffs, though he played professionally with the American Hockey League's Nova Scotia Oilers during the 1987-88 season.
An outstanding golfer, Edwards spent parts of his off-seasons participating in tournaments. He also held coaching positions in the National Hockey League, serving as the Los Angeles Kings' assistant coach and the Carolina Hurricanes' goaltending coach. He is now the general manager of the Saginaw Spirit of the Ontario Hockey League.