The German made a lightning start, breaking in the first game with some excellent ground strokes. Her lead did not last long though, as the Chinese broke straight back.
Li's forehand began to dominate the contest from the fourth game, in which she broke Goerges to take the lead. It was a backhand that eventually forced the error from the 18th seed.
It seemed as though neither player wanted to be in front, as Li now relinquished control of the set.
Goerges broke easily to get back on serve at 4-3 down, before both players held to bring about a tie-break.
The German brought up the first set point at 5-6, and looked to be about to clinch the opener as she took the upper hand.
However, she fired into the net to let the sixth seed off the hook. Li then capitalised on that lifeline by going on to secure the tie break 8-6.
The second set was all Li, as she steamrollered her way into the quarter-finals with a 6-1 triumph.