Amelie Mauresmo will face the first big test of her world number one status when she faces US Open champion Svetlana Kuznetsova in Filderstadt. Mauresmo, who replaced Justine Henin-Hardenne at the top of the world rankings, beat Lisa Raymond 6-4 6-1.
Kuznetsova cruised past Colombia's Fabiola Zuluaga 6-4 6-1.
Lindsay Davenport beat qualifier Jelena Jankovic 6-4 6-3 and will face Anastasia Myskina, who beat Elena Likhovtseva, in the semis.
Raymond lost in qualifying but gained a place in the main draw when Kim Clijsters withdrew and the American offered a stern challenge early on.
But Mauresmo broke for a 4-3 lead in the first set, claiming Raymond's serve after the American had led 40-0.
Mauresmo did not allow Raymond to hold serve at all in the second set and claimed victory in just 64 minutes.
"I was very satisfied, especially because my serve was very strong," said Mauresmo who struck eight aces.
"I feel no pressure because now I'm number one. I expected that."
Myskina, the third seed, needed three sets to oust fellow Russian Likhovtseva 4-6 6-0 6-2.