Rex Hartwig was born on 2 September 1929 in Culcairn, New South Wales. 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.
In 1953 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.
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 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.
|Runner-up||1954||Australian Championships||Mervyn Rose||2–6, 6–0, 4–6, 2–6|
|Runner-up||1954||U.S. Championships||Vic Seixas||6–3, 2–6, 4–6, 4–6|
|Runner-up||1953||Wimbledon Championships||Mervyn Rose|| Lew Hoad
|4–6, 5–7, 6–4, 5–7|
|Winner||1953||U.S. Championships||Mervyn Rose|| Gardnar Mulloy
|6–4, 4–6, 6–2, 6–4|
|Winner||1954||Australian Championships||Mervyn Rose|| Neale Fraser
|6–3, 6–4, 6–2|
|Winner||1954||Wimbledon Championships||Mervyn Rose|| Vic Seixas
|6–4, 6–4, 3–6, 6–4|
|Winner||1955||Wimbledon Championships||Mervyn Rose|| Neale Fraser
|7–5, 6–4, 6–3|
|Winner||1953||Australian Championships||Julia Sampson Hayward|| Maureen Connolly
|Runner-up||1953||U.S. Championships||Julia Sampson Hayward|| Doris Hart
|2–6, 6–4, 4–6|
|Winner||1954||Australian Championships||Thelma Coyne Long|| Beryl Penrose
|4–6, 6–1, 6–2|
|Runner-up||1954||French Championships||Jacqueline Patorni|| Maureen Connolly