The 29-year-old German was in sparkling form, firing 41 winners and making just 23 unforced errors to win 6-4 7-6 (4/7) after 90 minutes on court.
Goerges, who was runner-up to US Open champion Sloane Stephens in 2016, won the first set with her seventh ace, having broken serve in the very first game.
She broke again in the first game of the second set, before the world number three fought back to force a tie-break.
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With a thundering forehand proving her biggest asset, it was only fitting for Goerges, the number two seed, to seal the title with a forehand winner.
After the match, Goerges said her achievement felt "amazing".
She added on the WTA website: "It's not just about winning here, but the consistency I've had for the last few weeks and months. That makes me prouder, and I'm just enjoying every moment of it."
Wozniacki, meanwhile, vowed to get her revenge at the Australian Open in Melbourne later this month.
Quoted on the website, she said: "She played really well today, and she had a great end to last season too, so it's good to see her bringing that form into this year.
"I'll try to get my revenge in Australia!"
Goerges, ranked number 14 in the world, earned her back-to-back victories at the Kremlin Cup in Moscow and the WTA Elite Trophy in Zhuhai, while Wozniacki won the biggest title of her career in October at the WTA Finals in Singapore.
Elsewhere on the tour, British number two Heather Watson came through an early scare in her second qualifying match to reach the main draw at the Hobart International.
Despite dropping the first set, she fought back to beat Japan's Nao Hibino 4-6 7-5 6-3, and will face Romania's Sorana Cirstea in the first round of a tournament she won in 2015.
The 2016 champion Alize Cornet was dispatched in the first round on Sunday by Romania's Mihaela Buzarnescu.
At the Sydney International, fifth seed and world number 11 Kristina Mladenovic retired during her match against Australian wildcard Ellen Perez amid soaring temperatures in the city.
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