The 21-year-old Barthel, ranked 64th, closed with an ace on match point. She had a first-serve rate of 82 percent in the final.
Barthel, who won three qualifying and five main draw matches at Hobart, will play her doubles partner Anne Keothavong in the first round of the Australian Open in Melbourne on Monday.
"I have to relax now a little bit and of course I will celebrate," she said. "I've never been there (Melbourne Park) before, so I will look everywhere and see and then I will try to have a hit, try to get used to the courts."
She is beginning to believe in her ability to win big matches.
"I did it once now so I can do it maybe another time," she said. "I think I can go even one step further."