The American roared out of the traps, winning five games in a row and crushing any chance of resistance from the Chinese.
Zhang raised her game towards the end of the first set and made a decent fist of the second, but Williams's driving forehand and serving power was too much for the world number 43.
Williams will get the chance to avenge her Australian Open defeat to Ana Ivanovic in the semis after the Serbian 11th seed followed up her impressive win over Maria Sharapova with a thrilling 6-4 3-6 6-4 win over Spain's Carla Suarez Navarro.
Home fans were given something to shout about when Sara Errani reached the semi-finals with a superb 6-3 4-6 6-2 victory over world number two Li Na - her first career win against a player ranked in the top three.
1-Serena Williams (U.S.) beat Zhang Shuai (China) 6-1 6-3
6-Jelena Jankovic (Serbia) beat 3-Agnieszka Radwanska (Poland) 6-4 6-4
11-Ana Ivanovic (Serbia) beat 13-Carla Suarez Navarro (Spain) 6-4 3-6 6-4
10-Sara Errani (Italy) beat 2-Li Na (China) 6-3 4-6 6-2
- Sports & Recreation
- Ana Ivanovic
- Sara Errani
- Carla Suarez Navarro
- Maria Sharapova