The ninth seed has never been beyond the fourth round of her home Grand Slam but had recovered from a poor start to earn a winning position.
Stosur struggled on serve throughout the first set and handed Zheng the initiative, which she duly used to claim a 6-4 advantage.
A determined Stosur rallied to trounce her opponent 6-1 in the second to level the match.
With a passionate crowd in her corner at the Rod Laver Arena, the Aussie secured a double break to take complete control of the deciding set.
Stosur held a 5-2 advantage but twice failed to serve out the match as Zheng fought hard to win five successive games and leave the home crowd stunned as home interest in the women's singles came to an abrupt end.
The 28-year-old has missed out on the chance to play regular doubles partner Julia Gorges, who will now face Zheng in the third round.