Kvitova is one of four women who could be No. 1 at the end of this fortnight.
"I don't know who lost and who win," Kvitova said. "No, really, for me doesn't care."
Kvitova's fourth-round opponent will be former world No. 1 Ana Ivanovic.
Sharapova, who was last year's Wimbledon runner-up to the left-handed Kvitova, leveled 30th-seeded German Angelique Kerber 6-1, 6-2 in 87 minutes.
The former world No. 1 Sharapova, who captured the 2008 Aussie Open for her third career Grand Slam championship, will take on tough German Sabine Lisicki here on Monday.
A 12th-seeded Williams, meanwhile, dominated helpless Hungarian Greta Arn 6-1, 6-1 in a mere 59 minutes at Melbourne Park.
Leading 5-0 and a point away from winning the opening set, the former top- ranked Williams set-up for an overhead smash, only to shank it wide of the court. The powerful American screamed and put a hand over her face.
"It was an awkward smash. Then she missed one and I felt a little better," Williams said. "I felt like, 'Am I losing my mind out here?' Everyone sometimes hits a shot that's a little bit insane -- you just got to allow yourself to get over it."
The 13-time major champion Williams has now won her last 17 matches in Melbourne, where she titled back-to-back in 2009 and 2010 before missing last year's event because of a series of health issues.
"I'm nowhere near where I want to be," Williams said. "I'm just trying to play through it. A little rusty -- just trying to play through my rust."
A 14th-seeded Lisicki needed all three sets to overcome 18th-seeded Russian Svetlana Kuznetsova 2-6, 6-4, 6-2, while the 21st-seeded Serbian Ivanovic was a straight-set winner over American Vania King, 6-3, 6-4. The former top- five star Kuznetsova is a two-time major champ. The former No. 1 Ivanovic was the '08 Aussie runner-up to the Russian Sharapova.
Also advancing Saturday was Italian Sara Errani, who rallied for a 6-7 (6-8), 6-0, 6-2 victory over Romanian Sorana Cirstea. Errani will meet Zheng in the round of 16.
The former U.S. Open runner-up Wozniacki will face 13th-seeded former world No. 1 Jelena Jankovic, while the 11th-seeded Clijsters will battle fifth- seeded Chinese Li Na in a rematch of last year's Melbourne finale, which was won by Clijsters in three sets. Clijsters is a four-time Grand Slam champ, while Li captured her first-ever major title at the French Open last spring.
Also on Sunday, third-seeded Belarusian slugger Victoria Azarenka will face veteran Czech left-hander Iveta Benesova and eighth-seeded Pole Aggie Radwanska will encounter 22nd-seeded German Julia Goerges.
Azarenka titled in Sydney last week by beating Li in the marquee finale.