Japanese 13th seed Sayaka Takahashi gave a tough fight to seventh-seeded Saina and was almost on her way to the last eight, before Saina found her legs just in time to recover from a game down and win the three-game one-hour-five-minute marathon third round match 14-21, 21-18, 21-12.
It was an even more close and tougher affair for 11th seed Sindhu who had to play out of her skin to beat South Korean sixth seed Yeon Ju Bae 19-21, 22-20, 25-23 in one of her longest matches in recent times, lasting an hour and 16 minutes.
The 19-year-old Indian had to save three matchpoints and waste five before she could finally seal the tie in her favour to notch up her first win against Yeon in three meetings.
Sayaka looked in sublime touch as she easily clinched the first game. World No.7 Saina looked down and out trailing 8-13 in the second but slowly started getting back into rhythm when the reality of being ousted from the tournament hit her.
The 24-year-old finally levelled the game at 18-all and held on to the next three points to push the match into the decider.
It was equal till 7-all in the third game, but after that the Olympic bronze medallist found the right footing and form to crush her opponent in a matter of minutes and take a 2-0 lead in career meetings over the Japanese.
Saina will be up against World No.1 and top seed Li Xuerui of China next and the reigning Olympic champion has a 7-2 career advantage over the Hyderabadi.
Later, Sindhu played a tight first game but her World No.5 opponent managed to take away the game from 18-all. It was again extremely close again in the second game but Yeon's deceptive shots made sure she had two matchpoints before Sindhu could realise it.
However, the World No.12 Indian put her height to optimum use to eke out the next four points and take the game and push the match into the decider.
The decider also turned into another unbelievably close contest. But some excellent smashing and net play by the 19-year-old Indian saw her reach matchpoint at 20-17.
Some brilliant cross-court sliced smashes by the South Korean saw her level the encounter at 20-all. Yeon saved two more matchpoints and surprised Sindhu to go ahead to matchpoint. But Sindhu had nerves of steel to save that one last matchpoint and take the marathon encounter by winning the next three points.
Sindhu has an even tougher challenge lying ahead when she faces old foe and second seed Shixian Wang of China in the last eight. Though the Indian has an 3-2 advantage over Shixian, the Chinese won the previous two encounters.
Meanwhile, Manu Attri and B. Sumeeth Reddy's journey came to an end when they lost to South Korean second seeds Yong Dae Lee and Yeon Seong Yoo in the men's doubles third round. The World No.1 pair needed only 37 minutes to move past the Indian combine 21-12, 21-17.
Kidambi Srikanth will play his men's singles match later in the day.