The No.14-seeded Ivanovic was the first of the Serbian pair to advance, fighting back from 5-1 down and saving a set point down 9-8 in the tie-break to sneak out a 61-minute first set, then cruising through the second set to beat former World No.10 Flavia Pennetta in an exciting straight-setter, 76(9) 61.
"I didn't think so much about the score in the first set, I was just struggling to find my rhythm in the beginning," Ivanovic said. "Then I just tried to think of getting back into the match. I thought the first set was already gone, but then I started to play better, and then I basically played point by point.
"I didn't think I could come back in the first set, but I played well and stepped up when it was very tight. I could see her body language change in the second set, and then I started to play a lot better."
Ivanovic admitted she was cautious when she saw she was playing against Pennetta in her first match.
"We probably both thought it was a tough first round," Ivanovic said. "She's been playing really well lately and is such a nice girl. When I went on the court, I knew it was going to be very, very tough.
"But I really found my rhythm in the second set and played a much better match after the first set."
The No.8-seeded Jankovic was probably even more cautious - she had Anastasia Pavlyuchenkova, who had won three of their four career meetings. And Pavlyuchenkova blasted through the first set in just 30 minutes - but Jankovic battled back to make it past the former World No.13 in three, 16 64 60.
"I've been working pretty hard towards my goals and practicing pretty hard," Zhang said. "I've just been giving my best every time I'm taking the court - that's what I've been doing the past three weeks."
Also among the first round winners was Bojana Jovanovski, who was responsible for the only blemish in the 10-of-last-11 for Zhang (in the final of the WTA 125K Series event in Ningbo on Friday). Qualifiers Eugenie Bouchard, Polona Hercog and Galina Voskoboeva also made the second round.