Czech Pliskova, who won the Brisbane International in the build-up to the tournament, lost 7-6 (7-4) 7-6 (7-3) to Russian Anastasia Pavlyuchenkova.
Ukrainian Svitolina was thrashed 6-1 6-2 by resurgent two-time Grand Slam champion Garbine Muguruza of Spain.
Muguruza needed just 68 minutes to blast past Svitolina.
Former world number one Muguruza won the French Open in 2016 and Wimbledon a year later but has struggled for consistency since.
Now ranked 32, she overpowered Svitolina, hitting 31 winners to just nine unforced errors to set up a meeting with either Kiki Bertens or Zarina Diyas.
There was another surprise as Swiss sixth seed Belinda Bencic was blown away by Estonia’s Anett Kontaveit, losing 6-0 6-1 in only 49 minutes on Margaret Court Arena.
Kontaveit, the 28th seed, won the first nine games as she dominated last year’s US Open semi-finalist.
She will now play 18-year-old Pole Iga Swiatek, who defeated 19th seed Donna Vekic of Croatia 7-5 6-3. Prior to Melbourne, the teenager had not been past the second-round stage at a Grand Slam.
Pliskova’s conqueror Pavlyuchenkova, a quarter-finalist last year, joked in her on-court interview: “I’m really happy, but will realise it later because I’m still focusing on the next point.
“I did enjoy the match – to beat Karolina for the first time was amazing.
“I won the Australian junior title twice; it makes me think I can win the senior crown.”
The Czech player blamed the defeat on the errors she made.
“They were maybe not huge, but I did a lot,” she said.
“I think I was having quite a struggle with my serve, so the percentage was not there – not really many aces.”
Pavlyuchenkova will next play 2016 champion Angelique Kerber, who was made to fight by Camila Giorgi but managed to win 6-2 6-7 (4-7) 6-3.
It was a battle between Giorgi’s aggression and Kerber’s defence with the Italian’s 65 unforced errors key as the German 17th seed went through.
There was no slip-up from Wimbledon champion Simona Halep, who produced an impressive display in her 6-1 6-4 win over Kazakhstan’s Yulia Putintseva.
The Romanian fourth seed broke all of her opponent’s service games in the first set but was given a tougher workout in the second. Having exchanged breaks with Putintseva before breaking again for 4-3, she saved two break points in her next service game.
Halep eventually wrapped up victory in the 10th game when the Kazakh’s slice found the net. She will now face 16th seed Elise Mertens, who defeated American Catherine Bellis 6-1 6-7 (5-7) 6-0.
“It was a great year winning Wimbledon, but here it’s a different tennis,” said Halep, who reached the final in 2018. “I’m ready – I was ready when I got here.”