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Unseeded Collins ended Tunisian Ons Jabeur's dream run to set up a clash with Australian Open champion Sofia Kenin.
Novak Djokovic was made to work hard by Casper Ruud in blustery conditions.
Defending champion Nadal was stunned by Argentine Diego Schwartzman in the quarterfinals.
Former world No.1 Kim Clijsters said she was looking forward to getting more matches under her belt and improving, after losing 6-3, 7-5 to Briton Johanna Konta in the opening round of the Monterrey Open.
The 21-year-old Kenin, seeded 14th at Melbourne Park, converted her second match point against the twice Grand Slam champion, who double faulted on the final point, to end an engrossing contest.
The 26-year-old Muguruza would not have been on many lists of pre-tournament contenders but the class and fighting spirit that propelled her to the 2016 French Open and 2017 Wimbledon titles has come flooding back in Australia.
Sofia Kenin sent world number one Ash Barty spinning out of the Melbourne Park semi-finals 7-6(6) 7-5 on Thursday, crushing Australian hopes of a first home-grown champion at the Grand Slam in 42 years.
Muguruza stormed back into the Grand Slam big time with an emphatic 7-5, 6-3 win over Russian Anastasia Pavlyuchenkova to reach her first Australian Open semifinal.
The unseeded former world No. 1 won 6-3, 6-3 on Rod Laver Arena and faces 30th seed Anastasia Pavlyuchenkova of Russia in the last eight.
Nadal, a 6-3, 7-6 (7/4), 6-1 winner over Argentina's Federico Delbonis, miscued a shot that hit a ballgirl in the head, but he melted hearts when he apologised and gave her a kiss on the cheek.