Rex Hartwig was born in Culcairn, Australia. Both parents played tennis and at age 10 Hartwig played and won in a local tournament with his father. When he was 13 he began competing in afternoon competitions and took a job managing tennis courts in Albury. He formed a doubles team with Allan Kendall jr. and the team won the NSW, Victorian and Australian Junior titles.
He won the doubles in Wimbledon twice: In 1954 with Mervyn Rose and in 1955 with Lew Hoad.
In 1953 Australian championships he also won the doubles with Mervyn Rose and the mixed doubles with Julia Sampson Hayward. In 1954 he again won the mixed doubles title in Melbourne, this time partnering Thelma Coyne Long.
In 1953 he won the doubles title at the US Championships with Mervyn Rose, defeating Gardnar Mulloy and Bill Talbert in the final that lasted 77 minutes.Playing singles he made the final in 1954 but lost to Vic Seixas.
Hartwig was member of the Australian Davis Cup team in 1953, 1954 and 1955. In 1953 he played the doubles match with Lew Hoad in the Challenge Round against the USA and lost to Vic Seixas and Tony Trabert. This would turn out to be Hartwig's only Davis Cup defeat. In 1954 he defeated Seixas in the Challenge Round that Australia lost to the USA. In 1955 he made a significant contribution towards Australia's Cup win, playing 11 matches in six ties and winning all of them. He compiled a 12–1 win–loss record in the Davis Cup (6–0 singles, 6–1 doubles).
In November 1954 Hartwig won the singles title at the New South Wales Championships in Sydney. In the final he defeated countryman Mervyn Rose in three straight sets.
In November 1955 Hartwig turned professional by signing a contract with tennis promoter Jack Kramer for a fixed amount of $30,000 plus a percentage of the gate receipts of the professional tour.
Hartwig was known for his well-timed groundstrokes and his crisp and accurate volleys. Australian tennis player and coach Harry Hopman characterized Hartwig as a great stylist.
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