Olympic bronze-medallist, Saina, who got a bye and a walkover in the first two rounds, was off the blocks with a 21-14 10-21 21-10 win over Japan's Nozomi Okuhara in a women's singles match that lasted for an hour and seven minutes.
The Indian will next take on fifth seed Tzu Ying Tai of Chinese Taipei.
Eighth seed Sindhu, a two-time bronze winner at the World Championships, set up a clash with top seed Li Xuerui of China in the quarterfinals after brushing aside Macau's Teng Iok U 21-8 21-9 in another women's singles match at the Wuhan Sports Center Gymnasium.
Among other Indians, the men's doubles pair of Manu Attri and Sumeeth Reddy B sank 10-21 13-21 against third seeds Xiaolong Liu and Zihan Qiu of China.
The mixed doubles pair of Arun Vishnu and Aparna Balan also went down 13-21 5-21 to Kai Lu and Yaqiong Huang of China.
An All England finalist, Saina fought back from 3-5 and 4-6 in the first and third game to hand Okuhara her third defeat in as many encounters.