Potvin was drafted in 1990 by the Toronto Maple Leafs. He spent his first pro season with their AHL affiliate in St. John's. That year, he won the Baz Bastien Memorial Trophy as the top goaltender of the AHL and the Dudley "Red" Garrett Memorial Trophy as the league's Rookie-of-the-Year. To top things off, he tended goal in four games for the Leafs who saw what they liked thus clearing the way for the club to dispense with Grant Fuhr in favour of their new rookie netminder.

In his early years with the Leafs, Potvin was a workhorse who, in his first big-league campaign, carried his club to the semi-finals where they eventually lost to Wayne Gretzky and his Los Angeles Kings. By the time he'd completed his six-year run with the Blue and White, Potvin had more games played and wins than all other Leafs stoppers except for Turk Broda and Johnny Bower. He set a club record, leading the league in games played with 74 during the 1996-97 season. During that campaign, he faced more shots than any goaltender in league history.

With the signing of free agent Curtis Joseph, Potvin saw the writing on the wall and the Leafs finally dealt him to the New York Islanders.

After a short stay with the Islanders, Potvin was sent to Vancouver where his stay was just as short as in New York. Following to sub-par seasons with New York and Vancouver, Potvin made a triumphant return to the NHL in 2000-01 with the Los Angeles Kings where he was workhouse for the team during their playoff run.

In 2001-02 Potvin played in 71 games with the Kings posting a 31-27-8 record along with 2.31 GAA before battling injuries throughout the 2002-03 season. After parts of three seasons with the Kings, Potvin was acquired by the Boston Bruins in the summer of 2003. Potvin would appear in 28 games with the Bruins however would not be re-signed by the club following the 2003-04 season.