The 91st-ranked Preston beat world No.31 Parry 7-6 (7-4) 6-1 in an hour and 26 minutes in Beijing to reach the last 32.
In a composed performance, the 20-year-old Preston gradually assumed the ascendancy over her 24-year-old rival and ultimately converted four of eight break points to Parry's two from four.
The Australian held a decisive edge when it came for points won on first serve, claiming 70 per cent compared with the 22nd seed's 55.3 per cent.
And the draw might have opened up somewhat for Preston, who will next face Ukraine's Daria Signur, the world No.46 who upset 14th seed Jasmine Paolini of Italy in three sets in their second-round match.
Australia's other woman in action on Friday, Maddison Inglis, bowed out with a tight straight sets loss in the second round to Sara Bejlek.
The 20-year-old Czech overcame Inglis 6-3 7-5 in an hour and 33 minutes to reach the round of 32.
Inglis, ranked 140, went in as the underdog against the 20th-seeded Bejlek, but put up a stern fight in a fairly even contest.
The were separated only by two break-point conversions, wth Bejlek capitalising on five of nine, and Inglis three of six.
Bejlek won 66 per cent of her first-serve points compared with Inglis's 56 per cent, and won half of her second serve points while the Australian dropped to just 35.3 per cent in that category.
Among other matches on Friday, fourth seed Mirra Andreeva beat China's Yue Yuan 3-6 6-0 6-0, while fifth seed Linda Noskova of Czechia downed Romania's Elena-Gabriela Ruse 6-4 6-1.