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Hsieh, the world number 48, battled back from 2-5 down in the final set and halted Halep who served for the match at 5-3 in the decider.
It will be Hsieh’s first appearance in the last 16 of a Slam where she will face Dominika Cibulkova of Slovakia for a place in the quarter-finals.
“It’s my first win against a world number one,” said 26-year-old Hsieh.
“It’s amazing. I was 2-5 down in the final set but the crowd pushed me to fight.”
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