Pliskova and Osaka's exits mean two of the top three women's seeds are out of the running, clearing obstacles for the likes of Halep and 2016 victor Angelique Kerber.
Croatian 19th seed Donna Vekic also crumbled to lower-ranked opposition when she lost 7-5, 6-3 to Poland's Iga Swiatek, who is returning from a stress fracture in her foot.
The Spanish whiz blew his countryman Pablo Carreno Busta off Rod Laver Arena on Saturday, not even facing a break point in the 6-1 6-2 6-4 demolition. "I am confident that I am going to play better because every day in the third set I have been able to show a good level of tennis".More news: The Falcon and The Winter Soldier Allegedly Introducing the Thunderbolts
Carreno Busta became a spectator as Nadal raced through the set in 29 minutes and he then broke again early in the second set to inflict more pain.
"Every day is a different story".
"I did very well with my serve and started to hit some forehands".
While Nadal was a bit anxious about his inability to kill off his opponent on Thursday, he was unconcerned to hear that potential fourth-round opponent Nick Kyrgios had imitated his service action ticks during the Australian's match against Gilles Simon.More news: Four dead after 6.8 magnitude quake strikes Turkey
Nadal, who looked at his wife sitting in the audience, was asked not to worry about her. "Especially I need to convert the break points", said Nadal, who is on the trail of Federer's record for Grand Slam titles.
She shrugged off the departure of some of the tournament favourites, saying defeats can happen to anyone. "I was so scared for her, honestly".
Karolina Pliskova, Belinda Bencic and Elina Svitolina recorded comfortable wins as all of the top 10 seeded players in the women's draw advanced to the third round in Melbourne for the first time since 2007. "I don't know. I was just down".
Nadal won the game to go up 5-1 in the set, before claiming match point on a forehand victor.More news: Canada gears up to protect against coronavirus
For more sports coverage, visit the ABS-CBN Sports website. The 13-year-old was hit on her face by the Spaniard's shot during his second-round tie against Argentina's Federico Delbonis during the first Grand Slam of the year on Thursday.