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The Indian duo defeated World No. 2 pair of Kim Astrup and Anders Skaarup Rasmussen of Denmark, 21-16 21-19.
Sindhu lost to Singapore's Yeo Jia Min 16-21 21-17 21-23 in the second round.
One of the favourites for the gold medal, Satwik and Chirag, the reigning Asian Games champions and Commonwealth Games winners, squandered a first-game advantage.
The reigning Asian Games champions had qualified for the quarterfinals on Monday.
Satwik and Chirag won 21-15, 21-15 over the Chinese pair of Chen Bo Yang and Liu Yi in the final.
The Indians had on Friday beaten the South Korean duo of Lee Yu Lim and Shen Seung Chan.
Olympic-bound women's pair of Tanisha Crasto and Ashwini Ponnappa beat Chinese Taipei's Hung En-Tzu and Lin Yu-Pei 21-19, 21-17 to also reach the quarterfinals.
Ashmita Chaliha came from behind to enter the second round of with a hard-fought win over Ester Nurumi Tri Wardoyo of Indonesia.
Lakshya Sen's campaign ended after he lost to reigning world champion Kunlavut Vitidsarn of Thailand in the men's singles semifinal.
An inspired Tai Tzu Ying secured her first women's singles India Open title with a dominating straight-game win over Chen Yu Fei.
Results 1-10 of 61
