It was plain sailing for Goerges, who hit 19 winners during the first set. She served for it at 5-1, but there was a sting in the tail from the Chinese pro.
Zheng managed to claim one of the breaks back before holding her own, but could not stop the German from eventually serving out the set at the second time of asking.
The world number 40 seized the advantage early in the second set and did not let go, storming to a convincing 6-1 victory.
Both players played their best tennis in the decider, with powerful strokes coming from both ends of the court.
It was Zheng who made the crucial breakthrough, allowing her to serve for the match at 5-4.
However, Goerges dug deep and capitalised on some nervy serving to break back and keep her tournament alive.
After holding serve, it was now Zheng who was battling to stay in the tournament. Goerges earned three match points, and needed only one to set up a fourth-round encounter with the winner of Li Na and Sorana Cirstea.