Robson, 18, who reached the fourth round of the US Open earlier this month, saw off Chinese second seed Jie Zheng in straight sets, with the Briton's clinical edge seeing her capitalise on five of her six break-point opportunities.
The new British number one will face another Chinese opponent in the quarter-finals in the form of seventh seed Shuai Peng.
Jie Zheng was the only seed to fail to advance from the second round on Wednesday.
Peng, the home favourite, breezed to a 6-2 6-1 win over qualifier Nudnida Luangnam.
Third seed Sorana Cirstea defeated wildcard Ying-Ying Duan 6-1 7-6 (7-0) to set up a quarter-final clash with French eighth seed Alize Cornet, who advanced when Olga Govortsova retired after losing the first set of their contest 6-4, the latest victim of the gastro illness which has swept the event.
Chanelle Scheepers beat Bojana Jovanovski 6-4 6-1 while her next opponent, Urszula Radwanska, was also a straight-sets winner as Luxembourg's Mandy Minella was dispatched 6-2 6-3.
Taiwan's Su-Wei Hsieh beat compatriot Kai-Chen Chang 6-0 6-3. France's Mathilde Johansson overcame a second-set wobble to triumph 6-2 4-6 7-5 over China's Saisai Zheng.