He appeared in his first NHL game on January 3, 1998, replacing Richter seven minutes into a contest against the Washington Capitals. Cloutier stopped all 16 shots he faced to record his first NHL victory by a 3–2 score. He made his first NHL start the following game against the Carolina Hurricanes on January 6, 1998. Stopping 26 shots, he helped the Rangers to a 4–2 win. He played 12 games total in 1998–99, backing Richter up for the remainder of the season, recording 4 wins, 5 losses and a tie with a 2.50 GAA and .907 save percentage. Perhaps his most well-known performance as a Ranger was during a game against the New York Islanders on April 4, 1998, in which he fought opposing goalie Tommy Salo. With seven minutes remaining in a 3–0 loss, several fights broke out between players. While Salo tried to intervene in a fight between the Rangers' P. J. Stock and Islanders' Mariusz Czerkawski, Cloutier attacked the Islanders goaltender. The subsequent goalie fight resulted in Cloutier repeatedly punching Salo in the back of the head before taking it upon himself to stop. He proceeded to skate towards the Islanders bench, challenging the opposing players before being restrained by a referee.