Top seed Halep, who ended her wait for a major title at the French Open last month, won the first set, had the chance to serve out for the victory and earned match point on her opponent’s serve.
However, Hsieh’s unpredictable offence and never-say-die attitude paid dividends as she upset the world number one to secure a 3-6 6-4 7-5 victory.
It means only one top-10 seed, Karolina Pliskova, remains in the women’s draw, although Serena Williams (25) is still in contention.
Hsieh will meet either Dominika Cibulkova or Elise Mertens in round four.
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