The Olympic champion was forced to go through qualifying only two years after reaching the quarter-finals for the second time, in a career slump that saw her undergo surgery last year and she collapsed on the court with joy after the win.
The 22nd-seeded Keys pulled off an escape act worthy of Houdini in the second round, saving five match points against Anna Bondar, but did not have the magic this time around as she let the contest slip through her fingers in the final moments.
Zheng next faces either six-times major winner Iga Swiatek or Czech Marie Bouzkova, who play later on Saturday.
"Finally one time a bit of luck is on my side," said Zheng. "I'm so happy and I know in the last match she also did that comeback. It was a very dramatic match for me but we both showed up with very strong tennis."
Zheng dropped serve with a double fault in the fourth game and Keys broke her to love in the opening set's penultimate game as the American looked poised to roll through.
But Zheng flipped the script in the second set, fighting through the tiebreak before sealing it with a lethal strike from the baseline.
Keys had her foot on the gas in the third set but Zheng found the brakes, saving match point in the seventh game before getting the break with a forehand winner.
Keys' nerves began to unravel from there as she piled up errors before handing over the contest on match point with a shot just out of bounds.
