After two years training with Edwards in Sydney, Goolagong played at Wimbledon for the first time in 1970, when she was 18. In 1971, she won the women's singles titles at both the French Open and Wimbledon, creating a sensation and becoming an instant celebrity in Australia and around the world. In the Wimbledon final, she defeated Margaret Court, the only other Australian woman ever to win the title. She was the first Australian Aboriginal woman to achieve international fame in sport and the first Aboriginal person to do so in any sport other than football or boxing. In 1971, she was named Australian of the Year and the Associated Press Female Athlete of the Year.

During the 1970s, Goolagong won the women's singles title at the Australian Open four times. She was also runner-up at Wimbledon three times. She had no luck at the US Open, losing the final for four successive years (1973-1976) but never winning the title.

Goolagong's final Grand Slam title came at Wimbledon in 1980. By this time, she was a 29-year-old mother and shocked the tennis world by beating Tracy Austin in the semi-finals and her great rival Chris Evert in the final, to win her second Wimbledon and seventh Grand Slam singles crown.

Goolagong was also a member of the Australian teams which won the Fed Cup three times in 1971, 1973, and 1974. Other notable career achievements included winning the WTA Tour Championships in 1974 and 1976 and the Italian Open in 1973.

Goolagong retired in 1983. Over the course of her career, Goolagong won 43 singles titles and 9 doubles titles. Her career prize-money totalled US$1,399,431.

Following her marriage to Roger Cawley in 1975, Goolagong settled in the United States (in Naples, Florida). This led to some criticism in Australia. After living in the US for eight eight years, the couple bought a home at Noosa Heads, Queensland, in 1991, where they settled with their two children � daughter Kelly (born 1977) and son Morgan (born 1981).

In 1988, Goolagong was inducted into the International Tennis Hall of Fame.

Goolagong was awarded an MBE in 1972 and made an Officer of the Order of Australia (AO) in 1982.

Goolagong was a member of the Board of the Australian Sports Commission from 1995 to 1997 and since 1997 has held the position of Sports Ambassador to Aboriginal and Torres Strait Islander Communities.

Since 2000, Goolagong Cawley has made an increasing commitment to Australian women's tennis, which has fallen on hard times in terms of the glamour international events, and was appointed captain of the Australian Fed Cup team in 2002. In 2003, she was winner for the Oceania region of the International Olympic Committee's 2003 Women and Sports Trophy.