World No. 1 Saina could not get across fifth seed Tzu Ying Tai of Chinese Taipei, going down 21-16 13-21 18-21 in a 55-minute women's singles match.
Eighth seed Sindhu, who is playing her first tournament after missing action last month, too ran out of steam against top seed Li Xuerui of China, losing 21-11 19-21 8-21 in a match that lasted 52 minutes.
Olympic Games bronze medallist, Saina has always found it difficult against Tzu even though she has beaten her opponent five times in the past.
Saina had to fight back after lagging 6-10 early on to draw parity at 11-11. The Indian opened up a slender 16-14 lead at one stage only to see it blow away. However, the Indian secured five consecutive points after that to grab the opening game.
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In the second, Tzu didn't give Saina any chance as she slowly and steadily distanced herself from the Indian, before making a giant jump with straight five points to move to 14-7. She held her fort after that to bounce back into contest.
Going into the match with a 1-1 record, Sindhu did not waste any time as she zoomed to a 8-1 lead, a gap which Li could not bridge as the Indian conjured up hopes of a win by pocketing the opening game.
In the second game too, Sindhu opened up a 7-3 lead early on but Li clawed back at 9-9 and turned the tables with a 17-13 lead after that. Sindhu narrow the gap to 19-20 but Li grabbed the next point to roar into contest.