Näslund made his debut with the team two days following the trade against the Dallas Stars. As his desired jersey number 19 was already being worn on the team by Tim Hunter, the Canucks gave him number 22. Going pointless in his first nine games with his new club, Näslund recorded a hat-trick in the last game of the regular season, a 5–0 win over the Calgary Flames on 13 April 1996. The victory qualified the Canucks for the 1996 playoffs. He finished the regular season with a combined 22 goals and 55 points over 76 games between Pittsburgh and Vancouver. Näslund competed in his first NHL playoffs as the Canucks faced the Colorado Avalanche in the first round. He scored his first career NHL playoff goal in the final game of the series, opening the scoring against goaltender Patrick Roy on the powerplay. Colorado won 3–2 to eliminate Vancouver in six games. Näslund added two assists over the course of the series for three points total.