Stevens made his Tottenham debut at the start of the 1983-84 season, again against Ipswich, but this time was on the losing side. He was a first team regular that season, making 40 league appearances and scoring four goals, and played on the winning side in the 1984 UEFA Cup Final, scoring his penalty in the shootout against Anderlecht. He was also in the side that suffered an unlikely 3–2 defeat to Coventry City in the 1987 FA Cup Final.