World No. 9 Sindhu, seeded fourth here, was stunned 15-21 21-12 18-21 by the 38th-ranked Wardani in their first-ever face-off at the international level on Thursday night.
The double Olympic medallist lost to Thailand's Supanida Katethong, 12-21, 20-22.
The Indian pair went down 16-21, 21-11, 15-21 to China's Liang Wei Keng and Wang Chang.
In the final the Indian duo defeated a Chinese Taipei pair, 21-13, 21-19.
The world No. 8 Indian pair dished out an attacking game and also controlled the net well to outwit the Korean combination of Choi Sol Gyu and Kim Won Ho.
The Indian duo will face the Korean pair of Choi Sol Gyu and Kim Won Ho in the semifinals.
The men's doubles duo defeated a French pair 2-1 in Paris on Tuesday.
This is India' maiden medal in men's doubles at the Worlds.
World No. 7 Satwiksairaj and Chirag dished out a gritty performance to outwit local favourites and defending champions Takuro Hoki and Yugo Kobayashi.
Ishaan Bhatnagar and Tanisha Crasto also advanced to the second round of the mixed doubles event.