Hlavackova had not been beyond the quarterfinals of a WTA event before. Ranked 108th, she specializes in doubles, where she won the French Open in 2011 and finished runner-up at Wimbledon, the London Olympics and the U.S. Open last year.
Hlavackova and Meusburger will meet for the first time. In her third career final, Meusburger is looking for her first title.
"I hope it's going to happen tomorrow," said Meusburger, who also reached the final of the 2007 Gastein Ladies but lost to Francesca Schiavone.
The 86th-ranked Meusburger broke Knapp in the opening game but missed two chances to go 4-1 up. After four consecutive breaks, Meusburger held serve at 5-4.
The Austrian failed to serve out the match at 5-2 but broke Knapp immediately afterward when the Italian ended the match with two double faults.
"I didn't play spectacular tennis, I just tried to be consistent," said Meusburger, who hasn't dropped a set in the tournament. "I kept the ball in play and waited for her mistakes. These tactics have paid off."
In a match that included 20 breaks of serve, Hlavackova got treatment for a right ankle injury toward the end of the opening set. She came from 4-1 down to take the second into a tiebreaker before breaking Svitolina's serve three more times in the decider.