The teenage sensation secured a 6-4 6-4 victory to continue her phenomenal breakout year and become the youngest player to reach a WTA final since Czech Nicole Vaidisova in 2004.
"This is definitely unreal, my first final on the WTA", Gauff said after her win, according to Agence France-Presse.
Gauff fell in the final round of qualifying but claimed a spot in the main draw as a lucky loser, and took that opportunity all the way to her first-ever WTA quarterfinal, semifinal, and now final with her 91-minute victory over three-time Linz semifinalist Petkovic. "I guess Linz is my special place, giving me a lot of luck and a lot of happiness here".
"Not even in juniors did I ever get into something as a lucky loser - now I'm in the final".
The current world number 110 is set to climb to at least 80th in the rankings next week.
After the match, Osaka, 21, invited Gauff to join her winner's interview, in a moment that left both tennis players in tears.
The 2017 French Open champion showed her fighting spirit to reach a first singles final of the year after fending off a match point in the second set and another two in the decider. Andrea hit a lot of winners and put pressure on me.
"But honestly, I'm just grateful that I've been given the platform and I hope that I'm able to use this platform in the right way", Gauff added.
The youngest-ever victor of a WTA Tour title was two-time US Open champion Tracy Austin, aged just 14, at Portland in 1977.
The second-set was a more straightforward affair, though after breaking for a 3-2 lead, Gauff was twice forced to dig deep to save break-back points from Petkovic.
"When I was younger, I was just dreaming about winning tournaments and winning slams I guess, and I didn't think about all that would come with it", she said.