Goerges rallied from 3-0 down to take the first set against Wozniacki after breaking twice. But she lost that momentum as the top-seeded Dane leveled the match with two breaks of her own in the second set.
The 27th-ranked German player broke Wozniacki in the eighth game of the deciding set to lead 5-3 before serving out the match. Goerges, who beat Wozniacki in the Porsche Grand Prix final last month, had 36 winners to her opponent's 11.
"I beat her twice in two weeks, so I'm pretty proud of myself," she said.
"I'm really happy with my play on clay right now," Mattek-Sands said. "I feel like a true dirtballer."
Information from The Associated Press was used in this report.