Just three matches had been able to start on Wednesday because of the inclement weather, which arrived again to prevent the players from getting through the backlog, but only after Muguruza had suffered a shock defeat to Zhang Shuai.
Zhang, who had seen off Timea Babos in her first-round match earlier in the day, came through a two-and-a-half-hour battle with the reigning French Open champion and fifth seed Muguruza 7-6 (7-3) 3-6 7-5.
Muguruza was also playing her second match of the day, earlier beating Cagla Buyukakcay 6-3 6-2, but could not quite complete a comeback from 5-2 down in the decider as Zhang prevailed.
Anastasia Pavlyuchenkova won the only match to be completed on Wednesday, but her valiant effort against third seed Dominika Cibulkova on Thursday fell short in a 7-5 2-6 6-2 loss.
A left thigh injury saw seventh seed Timea Bacsinszky withdraw from her first-round match with Yulia Putintseva, who then went on to lose in three sets to Monica Puig. Puerto Rican Puig had routed Laura Siegemund 6-0 6-1 in her opening clash.
Eighth seed Barbora Strycova made short work of wildcard Fatma Al Nabhani in a 6-3 6-0 triumph. The Czech lost the first game of her second-round meeting with Sam Stosur before rain forced them off court.
Caroline Wozniacki was a first-round winner over Kiki Bertens 6-2 6-3, Elena Vesnina had to come from a set down to see off Christina McHale and Daria Kasatkina, Lauren Davis and Caroline Garcia also began their tournaments with wins.
Davis then won the first set of her second-round contest with Vesnina 7-5 prior to the rain stopping play.