Part of the first major wave of Europeans to star in North American hockey, he was a major star in the WorldHockey Association from 1974 to 1978. He scored at least 114 points in each of his four seasons in the upstart league, finishing third or fourth among overall scorers every time. He led the WHA with 85 assists in 1976–77, and tied Marc Tardif for the lead the next season with 89. Along with countryman Anders Hedberg and established superstar Bobby Hull, he played a starring role as the Jets won Avco Cup titles in 1976 and 1978. In the 1976 playoffs, he scored 26 points in just 13 games and was named WHA Playoff MVP. In the summer of 1978, Nilsson and Hedberg signed with the National Hockey League's New York Rangers for $2.4 million, further weakening the struggling WHA which would cease operations after just one more season. Nilsson's NHL career was marred by two significant injuries. The first was a broken ankle suffered when his skate blade got caught in a crevice in the Madison Square Garden ice as he was hit by Denis Potvin of the New York Islanders, which resulted in Nilsson bearing the entire force of the hit on only one leg. Although Nilsson has never characterized the hit as dirty and, in 2009, said, "He was always fair. But the ice was never great in the Garden, because they had basketball and other events. My foot got caught. It was a freak thing," the incident is nevertheless commemorated by the "Potvin Sucks" chant that takes place during every Rangers home game. Nilsson's second serious injury was to his knee while representing Sweden at the 1981 Canada Cup which caused him to miss the entire 1981–82 season. Nilsson was limited to 160 games in his three full seasons with the Rangers, though he scored an impressive 163 points in that time. He scored 8 goals and 16 points in the 1980–81 playoffs as the Rangers advanced to the semi-finals before being eliminated by their local rivals, the defending champion Islanders. After missing the previous season, he returned to the Rangers lineup for ten games early in the 1982–83 season.
Nilsson tested positive for ephedrine after Sweden's 4–1 victory over Poland on 6 April 1974, at the 1974 World Ice Hockey Championships. As a result, Sweden's win was vacated, and Poland was awarded a 5–0 walkover win. Nilsson was suspended for the remainder of the tournament.
