Barthel, ranked 64th, closed with an ace on match point. She had a first-serve percentage of 82% in the final.
The 21-year-old had to qualify to make the main draw and beat second seed Anabel Medina Garrigues, fourth seed Angelique Kerber and Australian fifth seed Jarmila Gajdosova on her way to reaching her first final.
Wickmayer, ranked just inside the top 30 in the world, was never in the game after the tall Barthel blitzed out to a 4-0 lead in the first set.
Barthel will meet Britain's Anne Keothavong in the first round of the Australian Open, while Wickmayer plays Galina Voskoboeva of Kazakhstan.