The 1979 Thunderbird Classic was a women's singles tennis tournament played on outdoor hard courts at the Arizona Biltmore Hotel in Phoenix, Arizona in the United States.

The event was part of the AAA[a] category of the 1979 Colgate Series.

It was the ninth edition of the tournament and was held from October 10 through October 14, 1979.

[2] First-seeded Martina Navratilova successfully defended her 1978 title by winning the singles event and earned $20,000 first-prize money.

[2][1] Martina Navratilova defeated Chris Evert 6–1, 6–3 Betty Stöve / Wendy Turnbull defeated Rosie Casals / Chris Evert 6–4, 7–6(7–4)