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.
Gauff showed plenty of variety in her game as she beat the 75th-ranked Petkovic, relying frequently on well-executed drop shots.
The Latvian has endured a miserable season and has dropped outside the top 70 but, working with former Wimbledon victor Marion Bartoli, this week has seen a resurgence.More news: OPEC oil production drops after attacks on Saudi installations
"I am not essentially the most assured with it however it labored nicely at present", she said. "I think I'll keep using it until it doesn't work so well anymore".
The American has secured the main draw spot at the upcoming Australian Open, with her coevals only preparing to hit the junior action in Melbourne.
After taking the opening set in a tiebreak, Gauff needed only one break of serve to wrap up the match in 97 minutes for her first career win over a top-10 player. "I've really gotten a lot of support from the crowd", she told a sellout audience in this upper Austrian regional capital.
"Today was my first top-10 win, so I'm super proud of myself for that", Gauff said.More news: PM Modi cleans Mamallapuram beach ahead of meeting with President Xi
Five-time major victor and former world number one Sharapova, 32, has been carrying a shoulder injury and hasn't played since a first-round exit at the US Open.
The youngest-ever victor of a WTA Tour title was two-time US Open champion Tracy Austin, aged simply 14, at Portland in 1977.
The American fought through in the final game to serve out victory, staving off three break points and coming through on her second match point.More news: Donald Trump Announces "Very Substantial" Partial China Trade Deal
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