Fifth-seeded Stephens had to complete a three-set semifinal win over former World No. 1 Caroline Wozniacki, and after a brief rest, returned to play the final.
The doubleheader was brought about by rain on Friday night when Stephens was leading 5-2 in the first set. She hadn't won a set in five previous meetings against Wozniacki, but upon resumption on Saturday she quickly corrected that, then held out against a strong comeback by the Dane and won 6-2, 2-6, 6-3.
"To win a tournament is amazing and I'm just really happy," she said. "It's definitely been a tough week, I've played some really tough players and to play this morning and come back and play the final ... it's the first time I've done that so I was really pleased with the way I was able to hold myself together and win this afternoon."
The Hobart International, where Stephens was expected to play beginning Sunday, said in a statement Saturday that Stephens had withdrawn due to a viral illness.
The 22-year-old Stephens was supported throughout the week by new coach Kamau Murray and mother Sybil Smith. Only moments after completing her win she took a call courtside from her grandfather who was watching the match at home in Florida with Stephens' grandmother, brother and uncle.
"The last time I won a tournament -- well, I've only won two -- but mom wasn't there so it was nice for her to see me win a tournament," Stephens said.
"Now (Kamau Murray) is really going to think he's like Coach of the Year but he's not," she joked. "We've just started and done well together, and I'm looking forward to the rest of the year and excited with what we have in store together."
Stephens began the final strongly, holding serve to love in her first two service games, then had to stave off breakpoints in each of her next two games. She had two chances to break Goerges at 15-40 in the 11th game, missed those but gained a third chance which she took.
Stephens then served out the set as Goerges began to look more uncomfortable, taking a bathroom break when the set ended.
The American broke Goerges in the third game of the second set and again in the seventh to lead 5-2 and again served out the set without difficulty. Goerges had played her typically aggressive game, serving six aces but making 33 unforced errors.
"I can't really complain with the way I played here to start the year with a new team," Goerges said. "It's one of the best starts I've had so far in my career."