Konta ousted fourth-seeded Peng Shuai 6-1, 6-3 in a brisk 68 minutes. Konta converted five of her six break chances and dropped serve just once in the match.
King was a 6-4, 0-6, 6-4 winner over Bojana Jovanovski, who won a tournament last week in Uzbekistan. Jovanovski dominated the second set, losing just 10 points, but King had a pair of breaks in each of the first and third sets to get out of the second round.
Local wild-card favorite Zhang Shuai eliminated sixth-seeded and defending Guangzhou champion Hsieh Su-wei 6-2, 6-2, taking 60 percent of the points in the match and piling up six breaks.
No. 2-seeded Alize Cornet defeated Karolina Pliskova 7-6 (7-4), 6-0, dropping only eight points in the second set and fourth-seeded Laura Robson posted a 6-3, 7-6 (7-4) win over Zheng Saisai.
Also Wednesday, No. 8-seed Monica Puig beat Galina Voskoboeva 6-3, 6-2; Zheng Jie edged past Timea Babos 7-5, 7-6 (7-1) and Yvonne Meusburger rallied for a 2-6, 6-2, 6-4 win over Vesna Dolonc.
The quarterfinals have King facing Puig and Robson playing Zheng in the top of the draw while Zhang takes on Konta and Meusburger goes against Cornet in the lower half.