Rice remained first-choice right back for the club as he played in the 1972 FA Cup Final as well. He was also a regular injury free presence for three full seasons being 1971–72, 1975–76 & 1976–77. Of the Double-winning side, he was the one who remained at the club the longest, taking up the role as club captain in 1977. As captain, Rice had the honour of lifting the FA Cup after Arsenal beat Manchester United in 1979, as well as losing two finals in 1978 and 1980. He is one of only 3 Arsenal players to have played in five FA Cup Finals (1970–71, 1971–72, 1977–78, 1978–79, 1979–80), the other two being David Seaman and Ray Parlour. He also led Arsenal to the 1980 UEFA Cup Winners' Cup Final, which Arsenal lost on penalties to Valencia.