Kennedy turned professional for Arsenal in November 1968. He made his first team debut ten months later, and went on to win the Inter-Cities Fairs Cup in 1970, the First Division and FA Cup Double in 1970–71, and then play on the losing side in the 1972 FA Cup Final. His form then declined, and he was sold to Liverpool for a club record £200,000 fee in July 1974, at the same time that Bill Shankly resigned as manager. He initially struggled at the club, but after manager Bob Paisley converted him to a left-sided midfielder he went on to help Liverpool to become the dominant club of English football from 1975 to 1982. During his time at the club Liverpool won the First Division five times (1975–76, 1976–77, 1978–79, 1979–80, and 1981–82), the FA Charity Shield four times (1976, 1977, 1979 and 1980), the European Cup three times, (1977, 1978, and 1981), and the UEFA Cup (1976), UEFA Super Cup (1977), and League Cup (1981). He also picked up runners-up medals in the FA Cup (1977), UEFA Super Cup (1978), League Cup (1978), and World Club Championship (1981) and won the "Match of the Day"'s Goal of the Season award in 1978–79.