Näslund subsequently joined the Penguins for the 1993–94 season. Due to teammate Bryan Trottier already wearing his Modo jersey number, 19, he chose number 29 instead. He appeared in his first NHL game on 5 October 1993 against the Philadelphia Flyers. Five days later, he registered his first NHL point, an assist, during a game against the Quebec Nordiques. His first NHL goal came the following month on 9 November 1993 in a 3–3 tie against the St. Louis Blues. The goal came in the first period on the powerplay against goaltender Curtis Joseph, assisted by Doug Brown and Marty McSorley. Upon entering the NHL, Näslund struggled and was admittedly frustrated with himself. As a result, he was demoted to the Penguins' International Hockey League (IHL) affiliate, the Cleveland Lumberjacks, on several occasions. He finished his rookie campaign with four goals and seven assists in 71 games. Although the Penguins qualified for the 1994 playoffs, Näslund did not participate in post-season play, being made a healthy scratch (non-dressing player), and watched as Washington eliminated Pittsburgh in the first round.