Watson was outclassed by the 25th seed as the Brit saw her serve broken once in the opening set and twice in the second on Court 2.
Goerges stamped her authority on the match in the fourth game as she capitalised clinically on a string of double faults from her opponent.
Watson was unable to force a response in the opening set, and the German was able to take it comfortably 6-3 with her powerful groundstrokes the key weapon.
Indeed, a flurry of stunning shots from the back of the court ensured that Georges seized the initiative once more in the first game of the second set, securing the break.
Watson recovered her composure to hold second time round, and even managed to haul herself back on terms at 2-2 with a fine break of her own.
But Goerges was unwavering thereafter and crashed a stunning forehand winner to seal another break in the seventh game of the set.
Watson had no further resistance left as Goerges was left to close out the match in nerveless fashion, taking the second set 6-4.
Goerges will next take on Arantxa Rus of the Netherlands in the third round, while for Watson it was further valuable experience gained.