The 22-year-old Barthel, ranked 45, battled for one hour and 56 minutes before sealing the victory with her 53rd winner of the day on her fourth match point.
World number seven Errani, bidding for her seventh singles title, suffered a second disappointment in Paris, after losing to Maria Sharapova in last year's French Open final.
Barthel, who defeated French crowd favourites Marion Bartoli and Kristina Mladenovic on her way to the final, seemed to be cruising to victory when she broke her opponent's serve to lead 2-0 in the second set.
She held on to lead 5-2 but the resilient Errani fought back by taking advantage of the German's nervousness, only to surrender in the decisive tie-break.
"It was a bit complicated to wrap it up but it was my first final in as big an event. I was feeling the tension," Barthel, who won her first title in Hobart last season, said.
"It has been a beautiful week. I was not expecting to win such a tournament. This will be a great year, I think."