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 made his senior debut for the club on 20 November 1954 against Arsenal. 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. He was not on the plane to Munich, having not been selected in the squad for the quarter-final second leg tie with Red Star Belgrade of Yugoslavia.