Hsieh simply refused to give up, eventually securing a gutsy 3-6 6-4 7-5 victory.
It means nine of the top 10 seeds have fallen in the first week, with seventh seed Karolina Pliskova the highest ranked woman left in the draw. Seven-time champion Serena Williams, the 25th seed, also remains in contention.
The unorthodox Hsieh fought back from 5-2 behind in the decider to complete the unlikely turnaround, digging deep at 0-30 when serving for a place in the last 16 with some stunning defensive play.
The world number 48 will face Slovakia’s Dominika Cibulkova, a 6-2 6-2 winner over 15th seed Elise Mertens, in the fourth round.