The American can make it 19 trips to the second week at the majors by winning on Saturday.
The Ukrainian got into the fourth round, saving five match points against Ana Bogdan on Court 14.
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Petra Kvitova's six career grass-court titles are most of any active woman.
Paula Badosa, who suffered a fractured vertebrae in her back earlier this season, retired from her singles match and withdrew from mixed doubles.
Andy Murray and Stefanos Tsitsipas will have to resume their anticipated second round match tomorrow.
"I love to watch [Novak] play, as much as I was loving to watch Roger play," Stan Wawrinka said.
