Näslund impressed in his third training camp with the Penguins, held prior to the 1995–96 season. He was labelled in the media as "Mr. September", referring to his ability to show promise before struggling once the season began. Due to the departures of All-Star left-wingers Kevin Stevens and Luc Robitaille from the Penguins, Näslund had an opportunity for a more prominent role with the club in 1995–96. He played on the second offensive unit with winger Jaromír Jágr and centre Ron Francis during training camp before being moved up to the first line with Mario Lemieux. He showed an immediate improvement, starting the season with 36 points in 29 games. He recorded his first NHL career hat-trick on 28 November 1995 in a 7–2 win over the Ottawa Senators. However, his production slowed later in the season; he was scratched on several occasions and was demoted to the third and fourth lines by February.