This is the first Grand Slam since the Open era began in 1968 to lose the top two seeds in both the men’s and women’s draws before the last eight.
The 45th-ranked Linette faces Karolina Pliskova next after the former world number one romped past China’s Zhang Shuai 6-0, 6-4.
Linette gave a sizeable contingent of red-and-white-clad Polish fans at Rod Laver Arena plenty to cheer, just 24 hours after they saw countrywoman and top seed Iga Swiatek bundled out.
Linette, 30, was almost overcome after reaching her maiden Grand Slam quarter-final in 1hr 57min.
“I don’t really believe it,” she said. “I still can’t believe it, I don’t know what happened.
“I’m speechless, really. I don’t know what to say.”
Belarusian Sabalenka never really looked like she would follow Swiatek, Garcia and the rest out of the first major of the year.
Along with third-seeded American Jessica Pegula, fifth-seed Sabalenka looks the woman to beat. Both are chasing a maiden major crown.
Sabalenka defeated dangerous 12th-seed Belinda Bencic 7-5, 6-2 to set up a last-eight clash against unseeded Donna Vekic, who beat 17-year-old Linda Fruhvirtova in three sets.
Hard-hitting Sabalenka sprinted into her first quarter-final at the Australian Open and said: “My whole life, it took me a little while to understand that negative emotion is not gonna help you on court.
“You have to just stay strong and believe no matter what and then do everything you can.”
Later on Monday, Novak Djokovic will have to defy his troublesome hamstring and the home crowd when he plays Alex de Minaur for a place in the quarter-finals.
Djokovic would normally be a hot favourite at Melbourne Park, where the former world number one is chasing a record-extending 10th Australian Open crown and 22nd major title.
But the 35-year-old Serbian has been struggling badly with a left hamstring injury ever since he arrived at the tournament.
He had heavy strapping on his thigh and required medical treatment in his three-set third-round victory over 27th seed Grigor Dimitrov.
Djokovic will also need to deal with what is bound to be a partisan home crowd at the 15,000-capacity Rod Laver Arena.
There is also fear of the unknown — Djokovic and 22nd-seeded De Minaur have never played each other before.
“Of course it’s a big challenge playing an Aussie guy here in front of his home crowd,” said Djokovic.
“I’m sure that the atmosphere will be electric and he’s going to have a lot of support, and he’s going to be pumped to try to win the match.”
Also in the men’s draw, which has lost six of its top 10 seeds, Russia’s Andrey Rublev plays Danish teenager Holger Rune in an encounter between the fifth and ninth seeds.
Roberto Bautista Agut of Spain goes up against unseeded Tommy Paul of the United States, while also in the last 16, Ben Shelton and J.J. Wolf face off in an all-American showdown.
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