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, faced 10 break points but recovered well to fend off nine of them against Petkovic in the semifinal, before sealing victory on her second match point.
"This is crazy," Gauff said. "I thought I was out in qualifying and now I'm here. Linz is my special place.
"This was one of the highest-level matches I've played. Andrea hit a lot of winners and put pressure on me.
"I was fighting for every point, even at break points down, I just tried to get the serve in and make her play a point."
Gauff 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.
Information from Reuters contributed to this report.