The 22-year-old Görges collected only her second career title to add to her 2010 Bad Gastein trophy, 17 years after Anke Huber won the second of her Stuttgart crowns in 1994.
"I don't quite know how I did it," admitted the German, who won with 7-6 (7/3), 6-3.
"It is always as if you have to climb a high mountain against Caroline. Now I have done it, I can't quite believe it."
Görges, who sent down 38 winners to Wozniacki's nine, will now break into the top world's 30 for the first time in her career.
It was Wozniacki's second final defeat in 2011 after losing to Russia's Vera Zvonareva in Doha in February.
The 20-year-old Dane was stunned in her bid for her fourth title of the year, after wins at Dubai, Indian Wells and Charleston, as Görges grew in confidence as the final wore on.
"Julia played really well," admitted the 20-year-old top seed.
"She was very aggressive and everything was going in. I tried everything but it wasn't enough. I'll go back to the practice court and try to be better next time."
Görges was only the third German to ever reach the Stuttgart final, but she showed no sign of nerves by taking the first set tie-breaker, after building up a 6-2 lead, and then broke Wozniacki in only the second game of the second set.
The Dane failed to cope with Görges' strong serve and powerful baseline shots, while the German kept her cool at the crucial stages.
She then served out for a 3-0 lead and never allowed Wozniacki to settle as she kept the world number one under constant pressure, backed by a vocal 4,800-strong crowd who cheered the new champion to her title.
Görges played way above her new ranking of 27th, which she will receive on Monday, and she drives off with the winner's prize of a brand-new silver Porsche sports car worth $111,000, which presents her with a luxury problem.
"I haven't driven a car for three months, maybe I should try it again with a normal car first," she suggested.
Görges' success marked a successful week for Germany's top women players, who enjoyed their best outing in Stuttgart for 27 years.
Four Germans reached the quarter-finals and with Andrea Petkovic set now to be ranked 15th, the host nation will have two top 30 players for the first time since 1999.
"This is great," said Germany's Fed Cup captain Barbara Rittner, whose team wiped out last year's finalists the USA 5-0 last weekend.
"It all fitted together just like a jigsaw puzzle for us in Stuttgart."