A wing half, Goodwin was signed as a trainee from Cheshire Schoolboys by Manchester United on 1 October 1953 as one of the Busby Babes.
He helped the club win the 1956 and 1957 league championships, and was a member of the United team that made a comeback from the Munich air disaster that claimed the lives of eight players and ended the careers of two others, to reach the 1958 FA Cup final, losing 2–0 to Bolton Wanderers.
In the 1963–64 season, a collision with former Leeds teammate John Charles in an FA Cup tie against Cardiff City caused him to suffer a triple fracture of his leg,[2] eventually resulting in his retirement from playing on 1 December 1964.
Goodwin went on to become a player-manager at Scunthorpe United, although he did not play many games due to his injury,[3] making six appearances and scoring one goal for the club.
He later relocated to Washington state, where he coached Tacoma Stars and started a travel agency on Vashon Island.