Nevin scored 21 goals as a rookie with the Toronto Maple Leafs in 1960–61 and finished second in the Calder Memorial Trophy voting to teammate Dave Keon.

He formed a line with Red Kelly and Frank Mahovlich, helping the Maple Leafs win the Stanley Cup in 1962 and 1963.

In 1964, Nevin was traded to the New York Rangers, along with four other players, in exchange for Andy Bathgate and Don McKenney.

Following his time with the Kings, Nevin would head to the Edmonton Oilers of the World Hockey Association (WHA).

[1] Nevin was one of the first players in the National Hockey League to wear contact lenses, beginning in the early 1960s.