Goerges made short work of the first set, breaking Vinci in the fourth and eighth games to take it 6-2.
Vinci fought back in the second set, however, breaking the German twice in succession to take control.
Goerges pulled one break back immediately, but it was not enough as Vinci served out the set at the third time of asking.
The German drew first blood in the third set, breaking Vinci in her opening service game, only to be broken back three games later.
The seventh game of the set was a mammoth one, which Vinci eventually won on her fourth break point to take control of the match.
The Italian then held her own serve before breaking Goerges once more to clinch the third set 6-3 and seal the win.