After playing his first Grand Prix event in 1970, Amritraj achieved his first significant success in singles in 1973 when he reached the quarterfinals at two Grand Slam events. At Wimbledon, he lost in five sets to the eventual champion Jan Kodeš and later that summer at the US Open, lost to Ken Rosewall after having beaten Rod Laver two rounds earlier.
Amritraj beat Björn Borg in the second round in the US Open in 1974 before losing to Rosewall in quarterfinals. In 1979, he lost in the second round of Wimbledon to defending champion Borg after being up two sets to one and leading 4–1 in the fourth set. He reached his career-high ranking in singles of world No. 16 in July 1980. In 1981, he reached the quarterfinals of Wimbledon before losing in five sets to Jimmy Connors after being up 2–0. He beat John McEnroe in the first round of Cincinnati Masters in 1984. Overall, he had five career wins over Jimmy Connors in their eleven matches.
Amritraj was part of the India Davis Cup team that reached the finals in 1974 and 1987. Amritraj had a career singles win-loss record 384–296, winning 16 singles and 13 doubles titles.