Nilsson won the world title in 1957 and 1962, finishing second in 1963 and 1967 and third in 1958 and 1965. He competed at the 1956, 1960 and 1964 Winter Olympics, and finished in fourth, fifth and second place, respectively. He was the best forward of the 1960 tournament and was selected to the all-star team at the 1962 World Championships. 