The Winnipeg Jets of the upstart World Hockey Association signed him and fellow countryman, Anders Hedberg and they would help take the Jets to two Avoc Cup Championships (1976 & 1978) and he was a two time Assists leader in the WHA. The Swedish Centre would never have less than 114 Points a season as a Jet and he was third overall in Points three years in a row (1975-76 to 1977-78). When the league folded he was cemented as the WHA’s all-time leader in Assists per Game with 1.15.
Nilsson (and Hedberg) would sign with the New York Rangers and he was poised to prove his worth in Gotham but a severe ankle injury after being by Denis Potvin reduced his skill set. A second injury to his knee would cause him to miss a full NHL season and his return was short lived.While Nilsson did not have that long a career his importance to the game of hockey cannot be discounted.