Kucera won 6-2, 6-3 after coming back from a break down in the first set, before embarking on a run that saw him take the next nine games and jump into a 4-0 lead in the second set. The 24-year-old Slovak, who is ranked No. 10 in the world, rediscovered his ground strokes, peppering the lines with powerful shots and then frustrating Muster by changing his options with clever drop shots.
Kucera's semi-final opponent will be the Spanish clay court specialist Albert Costa, who beat Fabrice Santoro of France 6-3, 6-4. For Costa, the world No 26, it will be his first semi-final of the year.
Muster, who was briefly ranked world No 1 in 1996, leads the tour with 40 tournament titles on clay, but he has not won on the surface in 18 months and the Austrian has slipped to No 25.
The turning point came in the sixth game, when the two players exchanged a spectacular series of diagonal drop shots. The rally ended with Muster hitting the net, Kucera went on to break Muster's serve and the Austrian never got back into the match.
"Once he takes over, he can put a lot of pressure on you and wrong-foot you," Muster said. "He played a lot of top spin and kept me far behind the baseline."
The German Open represents one of the major form guides for the French Open, the second Grand Slam event of the year which starts on 25 May. "I wouldn't say I am one of the favourites," Kucera said, "but if I am fit enough and I keep playing this well, sure I could win the French Open."Reuse content