Gauff will now play former French Open victor Jelena Ostapenko of Latvia in Sunday's final.
The Linz week has been a breakthrough for the world number 110 who will crack the top 100 on Monday, when she travels to Luxembourg for the last event of her season.
Gauff became the youngest woman to reach a WTA semi-final since Nicole Vaidisova won the Tashkent title in 2004, and will take on Andrea Petkovic on Saturday for a spot in the final.
"I wanted to leave the court because I lost", Gauff said of the moment during a September interview on Today. "My first final, a lot of firsts for me here, so I hope I can keep this going".
"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.
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.
Gauff saved 9 of 10 break factors and broke her opponent for Three-2 within the second set as Petkovic saved 5 break factors earlier than double-faulting on a sixth.
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 teenager earned her place in the field as a lucky loser from qualifying as Greek Maria Sakkari withdrew injured to start the week. That proved to be the lone break of the match as Gauff was never pushed to deuce in her final four service games.