He started his career at Luton Town, after five years with the Hatters moved to Plymouth Argyle, and after three seasons with Plymouth he moved to Wimbledon. In the 1988 FA Cup Final, in which Wimbledon famously upset Liverpool 1–0, Goodyear was adjudged to have fouled John Aldridge, which gave Liverpool a controversial penalty. Aldridge took it, but Wimbledon goalkeeper Dave Beasant saved it.