Gordon signed for Town's rivals Norwich City and made his league debut for them on 25 August 1984 in a 3–3 draw against Liverpool.
He found first-team opportunities limited during the following 1985–86 season but did score the goal that secured the Division 2 championship for Norwich in a 1–1 draw against Stoke City on 19 April 1986.
Gordon was capped by England under 21s towards the end of the campaign, but hampered his chances of future selection when he and his Norwich City teammate Robert Rosario broke curfew while away with the under 21s and went to a nightclub.
He was the first player to score in a live televised Football League match involving the Canaries", a 2–1 win over West Ham.
In total, Gordon played 261 games for Norwich (the majority of which were as a right-sided midfielder) between his 1984 debut and his final appearance on 2 November 1991.
[6] In just over three years he made only 11 appearances in all competitions for West Ham and had a six-game loan period, in 1996, at Millwall[7] before leaving to join AFC Bournemouth in August 1996 on a free transfer.