Both players took medical timeouts during the almost three-hour match.
Zhang took a medical time out after the second set ended and again after the fifth game of the final set when Svitolina was trailing 3-2. Zhang had received frequent treatment between games as well for a right shoulder or back ailment.
Svitolina broke Zhang's serve in the sixth game to level the set at 3-3, then fended off two break points in the following game before holding to lead 4-3.
Svitolina served for the match at 5-4 but Zhang broke to extend it. Svitolina hit a backhand passing shot to clinch the 11th game and take a 6-5 lead, then broke Zhang's serve in the final game, clinching the 2-hour, 55-minute match when Zhang hit a forehand into the net.
Svitolina will play Madison Keys in the fourth round.
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