Azarenka conceded both games in the opening set as she took it 6-2, before destroying the Swiss with a bagel in the second.
It was a comprehensive victory for the top seed, whose place in the last four in Beijing never looked remotely in doubt.
Azarenka will next take on French ninth seed Marion Bartoli, who beat Carla Suarez Navarro of Spain 6-0 2-6 6-4.
Second seed Maria Sharapova did not lose a single game as Angelique Kerber of Germany pulled out of their match at 6-0 3-0 down.
The fifth seed was unable to get going at all, and retired with an apparent injury as she headed for a second successive bagel.
It was not such a good day for third seed Agnieszka Radwanska, who was dumped out in straight sets by China's Na Li.
Li secured the 6-4 6-2 victory with surprising ease against the Pole. She will next take on Sharapova in the semi-finals.