Nadal, searching for a revival after injuries wrecked last season, was tested by France's Gael Monfils before winning 6-3, 6-3, 4-6, 6-4 to book a last-eight clash with Milos Raonic.
Nadal, 30, was also pushed to five sets by Alexander Zverev, 19, in round three, but he has survived to reach his first major quarter-final since the 2015 French Open.
The Spanish world number nine now has an excellent chance to add to his 14 Grand Slam titles after world number one Andy Murray and title-holder Novak Djokovic were both knocked out.
A day after defending women's champion and top seed Angelique Kerber also fell by the wayside, Williams beat Barbora Strycova 7-5, 6-4 to set up a last-eight meeting with Johanna Konta.
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The American great would gain much from winning in Melbourne, as she would overtake Steffi Graf's Open-era record of 22 Grand Slam titles and end Kerber's short reign as world number one.
"I have absolutely nothing to lose in this tournament," said Williams, 35. "Everything here is a bonus for me. Obviously I'm here to win. Hopefully I can play better, I can only go better."
Britain's Konta, the ninth seed, also reached the last eight with a perfect record in sets after a convincing 6-1, 6-4 victory over Russia's Ekaterina Makarova.
- 'Tough little cookie' -
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Despite the task facing her, Konta was delighted to be playing Williams, a childhood idol, for what would be her second straight Australian Open semi-final.