The No.119 Alexandrova put a first-set bagel behind her and served up one of her own to seal a 0-6 6-4 6-0 victory.
Petkovic, bidding to win a first title in three years, took just 25 minutes to wrap up the opening set in the second semi-final.
That proved to a false down for the German, as Alexandrova warmed to the task, breaking to lead 3-2 in the second set and going on to set up a decider.
Alexandrova blew a stunned Petkovic away in a final set which lasted only 22 minutes.
"When I arrived here and first saw the qualification draw, I thought I could finish in the second round, maybe reach the main draw," Alexandrova said.
"I thought that was my maximum. But now I'm standing here and playing the final tomorrow [Sunday]. I think it's amazing. It's unbelievable."
Giorgi will play in a Linz final for the second time after the aggressive Italian defeated Alison Van Uytvanck 6-3 6-4.