Wozniacki, a former No. 1 and two-time finalist at the US Open, has never advanced beyond the quarterfinals at the French. She looked distracted in her 6-4, 7-6 (4) loss to Goerges, picking dust from under her fingernails during a second-set changeover after losing her serve in the seventh game.
In the first set, Wozniacki broke Goerges in the fourth game only to lose her next two service games. She angrily thumped her racket on the clay after netting a backhand that allowed Goerges to pull ahead 4-3.
Goerges, who is ranked 72nd after once ascending as high as No. 18, overcame the sniffles, frequently pulling out a tissue to wipe her red nose.
"Today is very special as I haven't beaten a top-10 player for a long time," said Goerges, who advanced to the third round for the third time in five years. "I just told myself to be aggressive. It paid off in the end."
American Irina Falconi also was extended to three sets before advancing to the third round.
The Associated Press contributed to this report.