Stephens was leading Wozniacki 5-2 in the first set when rain stopped play on Friday, and when they resumed play on Saturday morning the American held on, edging the No.3-seeded Dane, 6-2, 7-6(3).
And she continued her winning ways later in the day in the final - Stephens, the No.5 seed, reeled off nine of 11 games from 4-5 in the opening set to run away with it against Goerges, 7-5, 6-2.
She held all 10 of her service games in the match, fighting off the only two break points she faced.
"You can never prepare for playing a set and then rain, then finishing the match the next morning and coming back again in the afternoon. You just have to keep going and do your best," Stephens said.
"Julia had been playing some really great tennis all week, but I knew if I just kept playing solid I could do it. I was pleased the way I was able to pull myself together and come back and play well.
"Just kind of going with the flow - that was pretty much it. Pretty basic."
Stephens, who has played some of the best tennis of her career during the Australian season in the past - she was a semifinalist at the Australian Open in 2013, after all, famously upsetting Serena Williams along the way - now has two WTA titles, her first coming in Washington DC last summer.
"We have a really long season - I have to play all the way until October - so to win a tournament in the first week of the year is amazing," Stephens said. "But I'm going to have many more opportunities throughout the year, and I'm looking forward to all of them. It's easier to look at it that way."
The American was asked if she was surprised how well she did for the first week of the season.
"I wouldn't say surprised - I wouldn't use that word. But the first week of the year you don't really know what to expect. I felt good coming into the tournament. I was excited - I think that really helped."
? WTA (@WTA) January 9, 2016