After converting her second match point, Goerges sank to her feet and then lay flat on the red clay as the crowd cheered for the first German winner of the country's biggest women's tennis event since Anke Huber in 1994.
Goerges won $111,000 and a sports car.
"I don't quite know how I did it," she beamed in a courtside interview. "Against Caroline it feels like you always have a mountain to climb and I did it."
Goerges, who briefly had trouble starting the car she was given, had lost both previous encounters with the Dane.
Sunday, however, Goerges pinned Wozniacki back from the start, playing the Dane's backhand constantly and forcing her into making errors.
The big-serving 22-year-old, ranked 32nd in the world, did not allow her 20-year-old opponent any chance to break and Wozniacki also struggled with Goerges's kicking serve.
With no break on either side the two went into a first-set tiebreak and the German opened up a 5-2 lead when Wozniacki put a crosscourt forehand into the net.
She grabbed the first set on her second opportunity when Wozniacki sent another forehand long.
In the second set, the confident Goerges upped the pressure and broke Wozniacki to open up a 3-0 gap.
Wozniacki, who has yet to win a grand slam, finally got her first break points at 3-1 but Goerges's forehand and a volley gave the German a 4-1 lead.
"Julia played very well, very aggressive and the balls were going in," said Wozniacki. "I tried everything today but it did not work. I'll have to go back on the practice court and make things better."
"Hopefully we will have many more matches in the future."
(Writing by Karolos Grohmann; Editing by Clare Fallon)