The second seeded Nehwal had lost to the fifth seed from Chinese Taipei in each of their five previous encounters and Friday's match in Wuhan was no different for the Indian player.
London Olympics bronze medallist Saina started the match slowly and found herself 10-6 down in the first game before rallying back to take the opener 21-16.
Tzu dominated the second set and easily won 21-13, but the decider proved to be a close affair.
With the scores locked 17-all and the match approaching an hour in length, Tzu thrashed a couple of winners to win the game and the match 21-18 after 55 minutes of high-quality action.
Nehwal's Indian compatriot P V Sindhu also fell at the quarter-final stage when she was knocked out by Chinese top seed Li Xuerui.
The eighth-seeded Sindhu tried her best against the Olympic champion but ultimately could not build on her momentum after winning the first set as Li won 11-21, 21-19, 21-8.
In the men's draw, top seeds Chen Long and Lin Dan both advanced to the last four as well, as Chinese players continued to dominate the event.
World number two Lin was the first of the Chinese men's singles players on court on Friday and needed 46 to get the better of Sho Sasaki – the two-time Olympic champion winning 21-17 21-13 46 minutes.
Malaysia's participation in the men's singles competition came to an end when Wei Feng Chong, the country's second-ranked player, fell short in his match against Houwei Tian.
The early exchanges of the match took place on a fairly even keel but after the Chinese player won the first game 21-18, he made short work of the world number 38, winning the second game 21-9.
In another other quarter-final, world number one Chen Long needed only 42 minutes to dispose of Chinese Tapei's Tien Chen Chou.
The world champion didn't need to be anywhere near his best but still comfortably won 21-10 21-11 against the fifth seed.
Seventh seed Zhengming Wang then made an all-Chinese affair in the semi-finals when he upset Korean fourth seed Wan Ho Son 21-14 21-19.