Heavy rain throughout the week in New Zealand's largest city had caused havoc with the schedule, forcing organisers to play the quarter-finals and both semi-finals on Saturday and move the final to Sunday.
The Dane struggled in her earlier quarter-final against the 19-year-old American wildcard Sofia Kenin before winning the rain-affected match 4-6 6-2 6-4 just before 4pm (0300 GMT).
She returned to centre court at the Auckland Tennis Centre at about 5.50pm and then comfortably accounted for American qualifier Sachia Vickery, who had earlier upset third seed Agnieskza Radwanksa, in the 6-4 6-4 win.
"I'm exhausted, if I'm being honest," Wozniacki told the WTA website after her semi-final.
"It's a tough start to the season - you kind of feel it after the first match... in the back, and the legs, and then we didn't play for a couple of days, and I said, 'Oh, it's nice.'
"Then coming out here and playing three sets this morning, and then two sets when we ran a lot -- I'm not 17 anymore, I can feel it for sure!"
Goerges, who lost to American Sloane Stephens in the 2016 Auckland final, was far more comfortable in both of her matches.
She beat Polona Hercog 6-4 6-4 in the quarter-finals before moving into the final with a 6-1 6-4 win over Taiwan's Hsieh Su-wei.
Wozniacki, who lost the Auckland final to Venus Williams in 2015 and has been a tournament regular in recent years, can move up to number two in the world rankings if she wins the title on Sunday.
"I definitely need a good massage tonight and some great food to just try and be as fresh as possible for tomorrow," she said.
"It would be amazing ...obviously, being here in another final means a lot to me, and I would love to make it a step further and win this tournament."
(Reporting by Greg Stutchbury; Editing by Sudipto Ganguly)
