Cai and Fu were pushed hard in the second game by the world number sevens but held on to keep their London 2012 bid on track with a 21-15 21-19 success at Wembley Arena.
Cai said after the 43-minute encounter that he had expected a close match.
Speaking through an interpreter, Cai said: 'Because we are really too familiar with each other, it was very important to have confidence in this game - in the main points, to compete and win them.'
Their semi-final opponents will be Malaysia's Koo Kien Keat and Tan Boon Heong, who won 21-16 21-18 against Isara Bodin and Jongjit Maneepong of Thailand.
Europe will be represented in the last four by Denmark's third seeds Mathias Boe and Carsten Mogensen, who beat Fang Chieh Min and Lee Sheng Mu of Chinese Taipei 21-16 21-18.
They will play second seeds Chung Jae-sung and Lee Yong-dae, convincing 21-12 21-16 winners over Indonesia's Mohammad Ashan and Bona Septano.
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