Vernon played in Calgary's minor hockey system and then played junior for the Calgary Wranglers in the Western Hockey League. In 1983, he was added to the roster of the Portland Winter Hawks for the Memorial Cup and starred in the tournament as the Hawks won the Memorial Cup.
During his junior career he was twice named WHL goalie of the year.
The Flames drafted Vernon 56th overall in the 1981 Entry Draft. Although he made two appearances for the Flames during the 1982-83 season, Vernon's full impact would not be felt until the 1985-86 season when he was handed the starting goaltending duties for the playoffs.
Vernon had spent most of the regular season playing for the Flames affiliates in Moncton and Salt Lake City but he played plenty in the playoffs, 21 games in all, as the Flames went to the Stanley Cup final, losing to Montreal.
From that point until 1993-94 Vernon was the Flames No. 1 goalie and, in 1987 Vernon won 39 games and helped the Flames win the President's Trophy for most points in the regular season with 105. The Flames lost in the playoffs to rival Edmonton but returned the following season to again win the President's Trophy and defeat Montreal in the Stanley Cup.
Vernon was a big part of the championship and Flames fans will remember his save in the first round, Game 7 against Vancouver when he stopped Stan Smyl on a breakaway in overtime.
Vernon would post a 16-5 record with three shutouts as the Flames would go on to defeat Los Angeles, Chicago and, finally, Montreal in the Stanley Cup Finals.
Vernon continued as the Flames top goaltender until he was traded to Detroit in 1994 for defenceman Steve Chiasson. He went to the Stanley Cup finals with the Red Wings, but lost to the New Jersey Devils.
In 1996-97 Vernon played most of the regular season as a back-up to Chris Osgood in Detroit but when the playoffs began, Detroit coach Scotty Bowman gave Vernon the starting job and the Red Wings went on to win their first Stanley Cup in 42 years. Vernon received the Conn Smythe Trophy as the playoff MVP.
The following season Vernon was traded to San Jose where he spent two full seasons before being traded to the Florida Panthers.
In 2000, he was claimed by Minnesota in the waiver draft but the Wild turned around and traded him to Calgary where he played in 59 games over the next two seasons before officially announcing his retirement on Sept. 13, 2002.