The American teenager secured a 6-4, 6-4 straight sets victory in Austria in a match which lasted just over an hour and 30 minutes.
Gauff, 15, won 71 percent of points on her second serve as she managed to grind her way past the German in impressive style.
She becomes the youngest player to reach a WTA final since Czech Republic’s Nicole Vaidisova won the Tashkent Open in 2004, also aged 15.
The 2017 French Open champion recovered after losing the first set to battle back and claim a 1-6, 7-6, 7-6 victory over the Russian.
Gauff, who made an odds-defying run to the Wimbledon last 16 in July, will provisionally climb into the top 100 when the WTA rankings are released next week, edging closer to automatic qualification for the Australian Open in January.
The American had initially failed to make the main draw of the tournament, losing in straight sets to Germany’s Tamara Korpatsch in the second round of qualifying on Monday, but is now playing in her first tournament since advancing to the third round of the US Open, when she lost to Naomi Osaka.