Knapp, who reached the last four in Slovakia and Colombia as well, will play Yvonne Meusburger of Austria.
Elina Svitolina of Ukraine will take on first-time WTA semi-finalist Andrea Hlavackova of Czech Republic.
The 69th-ranked Knapp avoided break points and converted all five chances to break Beck's serve.
The German had beaten Knapp in straight sets in Nuremberg last month.
Meusburger, coming off her second career final in Budapest last week, defeated Arantxa Rus of the Netherlands 6-1, 7-6 (1).
The Austrian failed to serve out the match at 5-4 before converting her first match point in the tiebreaker.
Meusburger played in the first Gastein Ladies final in 2007, and has since reached at least the quarter-finals every year.
Svitolina defeated Patricia Mayr-Achleitner of Austria 6-3, 6-0 for her second semi-final this year after losing in the last four at Cali, Colombia, in February.
Svitolina hit six aces and saved all four break points, while Mayr-Achleitner scored just four points in her three service games in the second set.
Hlavackova beat Austrian wild card Lisa-Maria Moser of Austria, 6-3, 7-6 (4).
The match was suspended for 30 minutes because of rain at 5-5 in the second set before Hlavackova wrapped up the win on her third match point in the tiebreaker.Results from the fifth day of the WTA Bad Gastein Open (x denotes seeding):
Andrea Hlavackova (CZE) bt Lisa-Maria Moser (AUT) 6-3, 7-6 (7/4)
Elina Svitolina (UKR) bt Patricia Mayr (AUT) 6-3, 6-0
Yvonne Meusburger (AUT) bt Arantxa Rus (NED) 6-1, 7-6 (7/1)
Karin Knapp (ITA x8) bt Annika Beck (GER x2) 6-0, 6-1