The Serb, chasing a record seventh title in Melbourne, will now face Denis Shapovalov in the next round. The French Open champion now meets Venus Williams after the 38-year-old rolled back the years to beat France's Alize Cornet.
Germany's Alexander Zverev wasted a flurry of opportunities before securing a 7-6 (5) 6-4 5-7 6-7 (6) 6-1 win over unseeded Frenchman Jeremy Chardy to book a place in the third round on Thursday.
In another titanic battle, Canadian Milos Raonic ousted 2014 champion Stan Wawrinka in four tightly-contested sets that all went to tie-breaks, while eighth seed Kei Nishikori was stretched to a draining five sets against Ivo Karlovic. Shapovalov has split his last six matches on hard court.
There's no previous matches between these two players.
US Open champion and fourth seed Naomi Osaka had it relatively easy, sweeping past Slovenia's Tamara Zidansek 6-2, 6-4 with the roof closed on Margaret Court Arena due to the rain.
The 33-year-old Hsieh, who plays with a double-handed grip on both sides and uses a mixture of spin and slice and drop shots to unsettle her rivals, reached the fourth round last year in Melbourne and at Wimbledon, where she beat top-ranked Simona Halep. Shapovalov has a chance to make the fourth round of a grand slam for the second time in his career. "He nearly had it for sure", said the eighth seed, a three-time quarter-finalist at Melbourne Park.
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Men staying in the hunt included 11th seed Borna Coric of Croatia and Spain's 23rd seed Pablo Carreno-Busta.
Novak Djokovic extended his Grand Slam winning streak against lefthanders with a 6-3, 6-4, 4-6, 6-0 win over Denis Shapovalov on Saturday in the third round of the Australian Open.
Raonic swept to 3-0 and 5-1 leads in the tiebreaker but Herbert rallied to level at 5-5.