Gauff is the youngest woman to reach the semifinals at a WTA event since Nicole Vaidisova won in Tashkent in 2004.
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.
The 15-year-old, in the main draw as a lucky loser after initially failing to qualify, produced another demonstration of her enormous potential by claiming her first victory against a top-10 player.
"I've had a lot of luck and happiness here", she added.
"This is insane, I thought I was out of the tournament in qualifying", said the American.
"Linz is my particular place".
"First time in my life, even in juniors, that I got into something as a lucky loser and now I'm in the final", said Gauff.
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Gauff saved nine of 10 break points.
'This was one of the highest-level matches I've played.
Gauff was never threatened by her more experienced opponent, who owns titles this season at St Petersburg and Madrid and reached the Beijing semi-finals last week before returning to Europe.
Her mother arrived in time to watch her daughter, flying in from Luxembourg after arriving from Florida.
But she only got into the event as a lucky loser after an injury to former Wimbledon victor Angelique Kerber.