Curtis Joseph signed as a free agent with the St. Louis Blues on June 16, 1989. He joined the Blues that season and went 9-5-1 in 15 games. He made his NHL debut on January 2 against the Oilers and earned his first win on January 30 against the Islanders. In 1990-91, Curtis joined the Blues full-time as Vincent Riendeau's goaltending partner and helped the team improve 22 points under coach of the year Brian Sutter. In 30 games, Curtis went 16-10-2 with a 3.12 goals-against average and a 89.8 save percentage. In 1991-92, Curtis took over the Blues starting goaltending position and went 27-20-10 in 60 games. He posted a 3.01 GAA, a 91.0 save percentage and earned his first shutout on December 19 against the Sharks. He also recorded nine assists, the second most ever by a goaltender. In 1992-93, Curtis went 29-28-9 in 68 games and posted a 3.02 GAA with a 91.099 save percentage (team record). In the playoffs, he helped the Blues reach the second round of the playoffs with a 7-4 record and 2.27 GAA. He set team records with two consecutive shutouts (tie), a 174:18 minute shutout sequence and 105 straight saves in the first round against the Blackhawks. On May 3, he set a team record with 61 saves in a game in the second round against the Maple Leafs.
In 1993-94, Curtis set team records for games played by a goaltender (71, since broken), minutes (4,127, since broken), wins (36, since broken), shots against (2,382) and saves (2,169). That year, he played in the mid-season All-Star Game in New York. In the shortened 1994-95 season, Curtis went 20-10-1 with a 2.79 GAA and 90.2 save percentage. By season's end, he ranked second all-time on the Blues games played (280) and wins (137) lists and first on the club's assists by a goaltender (17) list.
On August 4, 1995, Curtis' rights was traded with the rights to Mike Grier to the Edmonton Oilers for a pair of first round draft picks. After starting the year in the IHL, Curtis signed with the Oilers in January and played 34 games down the stretch (15-16-2). At season's end, Curtis won the Top First Year Oiler award. In 1996-97, Curtis led the Oilers to their first playoff berth in five years. Curtis played 72 regular season games and went 32-29-9 with a 2.93 GAA and six shutouts (team record). Curtis won both the Oilers' Zane Feldman Trophy (team MVP) and Most Popular Player award. In the playoffs, Curtis led the team to the second round with a first round upset over the Stars. Curtis had two shutouts in the first round against the Stars, including a 43-save overtime victory on April 25.
In 1997-98, Curtis broke the Oilers' shutout records for a single season (8) and career (14). He won his second Oilers' Most Popular Player award and posted a 29-31-9 record. In the first round of the playoffs, Curtis posted back-to-back shutouts in games six and seven to eliminate the favoured Avalanche. Extending into the second round against the Stars, Curtis set the team record for longest consecutive shutout streak at 166:54 minutes. In that series against the Stars, Curtis starred in a 2-0 shutout win in game two as well as a 1-0 overtime loss in game three.
On July 15, 1998, Curtis signed as a free agent with the Toronto Maple Leafs. In his first year with his new team, he helped the Maple Leafs improve 28 points to reach the playoffs for the first time in three years. Curtis' 34 wins as well as the team's 45 wins were both team records. He won the team's Molson Cup Award, tied a team goaltender record with five assists and was selected to play in the mid-season All-Star Game (missed due to an injury). In the playoffs, Curtis helped the Maple Leafs reach the Eastern Conference finals before losing to the Sabres.
In 1999-2000, Curtis led the Maple Leafs to a Northeast Division title with 45 wins (tied team record) and 100 points (new team record). Curtis himself improved on his team record with 36 wins. During the season, Curtis recorded his 25th career shutout on November 3, played in his second All-Star Game on February 6 and won Player of the Week honours on February 28. He won the King Clancy Trophy for his leadership qualities and humanitarian contributions and won his second Maple Leafs' Moslon Cup Award. In the playoffs, Curtis helped the team reach the second round.
In 2000-01, Curtis went 33-27-8 with a 2.39 GAA, a 91.5 save percentage and six shutouts. In the playoffs, Curtis won back-to-back shutouts in the first two games against the Senators. From games one to three, he set a personal best with 223:41 minutes of shutout hockey.