Svitolina suffered from inconsistency on serve throughout the match, firing five aces but making seven double faults.
Other action on Center Court saw Germany's No. 3 seed Angelique Kerber defeat Madison Keys 6-0, 4-1 after the American retired injured.
Kerber now faces Australia's Ashleigh Barty, who defeated local hero Zheng Saisai 4-6, 6-1, 6-2 in a little over two hours.
Willed on by a partisan home crowd, Zhang twice broke Barty's serve on her way to winning the first set. However, the Shaanxi native couldn't maintain that momentum, allowing 2018 Wuhan Open runner-up Barty to take the following two sets with relative ease.
After a spot of rain, No. 5 seed Petra Kvitova got her Wuhan Open off to a winning start, beating Serbia's Aleksandra Krunic 6-3, 6-4.
"I'm very satisfied with how I played today," said Kvitova, who hit 13 aces during the course of the match. "My serve helped me a lot, and I was very pleased with that."
The Czech star's reward is a third round tie against Russia's Anastasia Pavlyuchenkova, who bested No. 12 seed Kiki Bertens of the Netherlands 6-4, 6-2.
Spain's Garbine Muguruza also secured safe passage to the third round, comprehensively defeating Switzerland's Viktorija Golubic 6-0, 6-1 in just one hour.
"I started playing at a very high level and I maintained that throughout the whole match. I felt like I was not giving her a lot of options, and I was finding the right shots, and it was a pretty good match," Muguruza told Xinhua after her victory.
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