The native of South Porcupine, Ontario entered the Toronto Maple Leafs' sphere of influence with the Shopsy's peewee team and was eventually a junior standout with the OHA's Marlboros. During his first two pro seasons he played the odd game for the Maple Leafs but eased his way into the pro game with the senior Chicoutimi Sagueneens and the AHL's Rochester Americans.

Nevin scored 21 goals as a rookie in 1960-61 and finished runner-up in the Calder trophy voting to teammate Dave Keon. The hard working forward played solid two-way hockey for the Leafs playing with Red Kelly and Frank Mahovlich and helped them win the Stanley Cup in 1962 and 1963. In February 1964 he was part of the package assembled to acquire star forward Andy Bathgate from the New York Rangers.

Nevin played over seven years in New York and topped the 20-goal mark five times. He helped the Blueshirts become one of the top outfits in the NHL and registered 107 points in 1970-71. A respected leader on the ice and in the dressing room, Nevin began a six-year run as team captain in 1965-66. His finest season for New York came in 1968-69 when he scored 31 goals playing on a line with Dave Balon and Walt Tkaczuk.

In May 1971, Nevin was sent to the Minnesota North Stars for Bobby Rousseau and provided leadership and sound two-way play for his new club. On June 13, 1973, he was claimed by the Los Angeles Kings in the Reverse Draft and hit the 20-goal mark for the first time in three years. The next year he registered a personal best 72 points as the Kings set a franchise record with 105 points. Nevin scored 55 points the next season before jumping to the WHA. After playing thirteen games for the Edmonton Oilers in 1976-77, the classy veteran retired after breaking his collarbone. He joined the Kings as an assistant to coach Bob Pulford and later helped the
Metro Toronto Oldtimers to the World Championship in 1984.