Peng, the No. 8 seed, defeated fourth-seeded Sloane Stephens 6-2, 6-3 in 69 minutes. Peng had four breaks in the first set, when Stephens managed just eight points in four games serving and two more in the second.
Oprandi was a 6-3, 3-4, 6-0 winner over Zheng Jie. Oprandi controlled the third set, winning 66 percent of the points on serve and 61 percent off Zheng's serve.
Friday's semifinal will be the third career meeting between Peng and Oprandi. They split the first two, including a straight-set win by Oprandi earlier this year.
Rain earlier in the week pushed the schedule back so there were two second-round matches Thursday.
Second-seeded Roberta Vinci defeated Yulia Putintseva 6-3, 5-7, 7-2 and Jamie Hampton upset No. 5-seed Kirsten Flipkens 6-4, 3-6, 7-5.
The other two scheduled quarterfinals were postponed because of rain.
Hampton and Vinci are to meet in a quarterfinal Friday after a quarterfinal between seventh-seeded Varvara Lepchenko and Kaia Kanepi. The winners of those matches will play in the semifinals in Friday's last scheduled match.