Zheng raced into an early 4-0 lead in the first set, displaying some impressive footwork to move around the court much quicker than her opponent.
Bartoli composed herself to fight back to 5-3, before Zheng finally took the set 6-3.
The second set began much more evenly, with Bartoli trying to add some aggression into her play.
Zheng handled the increased pressure well and, after making a string of unforced errors, broke serve twice to take the second set 6-3 and the match overall.
Zheng now heads into the fourth round of the Australian Open.