After Mona Barthel's exit, Beck was the highest seed left in the draw, but she was a distinct second best for the hour she spent on court with Knapp. Beck had won the pair's only previous meeting, in Nürnberg last month, but Knapp settled the score in emphatic fashion, her positive approach, particularly off the backhand wing, powered her to a 60 61 win.
"The score made it look easy, but it was a tough match," Knapp said. "I played Annika a month ago and she beat me, so she's obviously a great player.
"Today was not easy and I tried to be aggressive throughout the match and I think that was the key to my win."
Meeting Knapp for a place in the final will be home favorite Yvonne Meusburger.
In seven visits to Bad Gastein, Meusburger has never fallen prior to the quarterfinals, winning 18 matches along the way. Number 18 came against Arantxa Rus, who despite a stubborn rearguard action in the second set, eventually went down, 61 76(1).
"I've never played against Arantxa before and it's always tough to face left-handers," Meusburger said. "She hits with a lot of topspin and her backhand was very strong, especially in the second set.
"But I always felt comfortable, even when she was playing better, and I think my tactics worked really well today."
Mayr-Achleitner, a runner-up in Bad Gastein two years ago, was broken in the opening game and faced an uphill battle from then on, slipping to a 63 60 defeat after just over an hour.
"I felt quite sluggish and never really got my feet moving today," Mayr-Achleitner said. "It's still been a positive week and I'm feeling good for the rest of the summer. Next I have a couple of ITF events in Germany befre heading to America to prepare for the US Open."
Wildcard Moser gave a better account of herself, fighting back from 5-3 down to extend Hlavackova to a second set tie-break. However, this was only a temporary reprieve as the Czech overcame this setback - and a rain delay - progressing to her maiden WTA semifinal with a 63 76(4) victory.