As part of the "The Hot Line" with teammates Bobby Hull and Anders Hedberg that played from 1974 to 1978, Nilsson won two Avco World Trophies as WHA champions with the Winnipeg Jets.

[4] At the time the Buffalo Sabres of the National Hockey League owned Nilsson's NHL rights, but by going to the WHA there was no compensation required.

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.

It was a freak thing," the incident is nevertheless commemorated by the "Potvin Sucks" chant that takes place during every Rangers home game.

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.

Nilsson tested positive for ephedrine after Sweden's 4–1 victory over Poland on 6 April 1974, at the 1974 World Ice Hockey Championships.

The players alleged that the NHL and its teams violated the Racketeer Influenced and Corrupt Organizations (RICO) Act by colluding with Eagleson to enable him to embezzle from the National Hockey League Players' Association (NHLPA) and that the four-year statute of limitations in civil racketeering cases began when Eagleson was indicted in 1994.