Dangerous Czech Tomas Berdych, a two-time Melbourne Park semi-finalist, also powered into the last eight, demolishing Italy's Fabio Fognini 6-1, 6-4, 6-4.
His reward is a clash with either Swiss maestro Roger Federer or unheralded Hungarian Marton Fucsovics for a place in the semi-finals on Wednesday.
Germany's Kerber is the only Grand Slam champion left on the women's side of the draw, and she was given a big fright as she chases her second Melbourne Park crown after beating Serena Williams in 2016.
At one point Kerber was serving to stay in the match, but she bounced back to win 4-6, 7-5, 6-2.
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"Credit to her, she played unbelievable. I was running everywhere," said Kerber, who had a poor 2017 after starting the year as world number one.
"I was just trying to focus on every point."
Hsieh, ranked 88, was always going to be a threat after knocking out world number three Garbine Muguruza and the dangerous Agnieszka Radwanska en route to the fourth round.
Seeded 17, she flattened French eighth seed Caroline Garcia 6-3, 6-2 in just 68 impressive minutes.
"I feel like I'm playing just solid, consistent tennis," said Keys, a US Open finalist last year. "I think today was a good example of that. I think I served well. I think I returned well."
The 22-year-old added: "Right now I'm definitely really enjoying my job."
Whoever wins that match will have a potential semi-final against world number one Simona Halep, although the Romanian first has to get past Japan's Naomi Osaka on Margaret Court Arena.
The final women's match sees sixth seed Karolina Pliskova take on fellow Czech Barbora Strycova, seeded 20.
- Enjoying it -
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Berdych, a semi-finalist in 2014 and 2015 at his most successful major, easily beat Fognini with the 32-year-old saying: "I'm really enjoying every single moment on court.
"I'm feeling good and healthy."
He is now in his seventh Australian Open quarter-final with Federer, who knocked him out in the third round last year, looming.
The Swiss maestro, 36, has made at least the last eight every year since 2004, bar a hiccup in 2015, with the odds of him doing so again heavily stacked in his favour.
Fucsovics has never beaten anyone ranked higher than 13th and is making his tournament debut.
Novak Djokovic is also in action in a night match as he looks to reach the last eight in Melbourne for a 10th time, with a tough test against talented Chung Hyeon.
"He's playing great. He's fit. He doesn't have too many holes in his game," he said.
The winner will face either Austrian fifth seed Dominic Thiem or American surprise packet Tennys Sandgren.