Zheng, a wildcard entry in Beijing, finally notched her first straight-sets win of this year's tournament, having needed more than 10 hours on court to get to the quarter-finals.
The world number 54 sent the crowd roaring as she punched winners down the line, though the seventh-ranked Svitolina came back fighting to force a second-set tiebreak.
Zheng double-faulted on the first point but crawled her way out from a 0-2 deficit and fell onto her back victorious after winning her second match point.
"Truthfully, because I really wanted to grab this win, I was really nervous," the 24-year-old told the crowd.
"I played really aggressive in important moments," she said, adding that her opponent "raised her level" in a tight second set.
Svitolina made just 13 unforced errors over the one-hour-and-47-minute match, but was outgunned by 48 winners from the 2024 Olympic champion.
Mertens upsets Swiatek
Mertens, the world number 19, beat Poland's Iga Swiatek 7-6(0), 6-3, overcoming some nerves to dump out the 2023 title winner.
"I tried to be consistent. She's a great player, so I had to really push myself," said Mertens, who had lost both of her two previous matches against eighth-seeded Swiatek.
"It was really nerve-wracking at the end, but I kept myself calm... I just can't believe it."
The 30-year-old was the evening's better technician, making just 11 unforced errors to Swiatek's 34 across the one-hour-and-50-minute affair.
Mertens had surged into her singles quarter-final after beating third-seeded Coco Gauff, also in straight sets.
