Nadal will next play sixth-seeded Marin Cilic, who collected his 100th Grand Slam match win with a 6-7 (2), 6-3, 7-6 (0), 7-6 (3) victory over No. 10 Pablo Carreno Busta.
Wozniacki could return to the top ranking if she reaches the semifinals at least and a combination of other results go her way.
The Columbian pair didn't break a sweat in the third round of the men's doubles as they rode off an easy win against Paes-Raja, defeating them 6-1,6-2.
Federer earned his 17th victory over Gasquet in the 19th encounter between the two players.
Seeking a record seventh title in Melbourne, Djokovic is set to take on Chung Hyeon of South Korea, who stunned Germany's Alexander Zverev 5-7, 7-6 (7-3), 2-6, 6-3, 6-0.
The fiery Australian reportedly pulled out of the doubles event believing he has a serious chance of winning his maiden Grand Slam title in the singles at Melbourne Park.
Five-time major winner Sharapova was back at the Australian Open for the first time since 2016, when a failed test for Meldonium led to a 15-month doping ban.
The Indian duo will now take on Colombian duo of Juan Sebastian Cabal and Robert Farah for a place in the quarter-finals.
The third set between Davis and Halep took 2 hours and 22 minutes and momentum swung, with 11 service breaks and two medical timeouts.
Wozniacki faced criticism during her first stay at No. 1 — which included year-end top rankings in 2010 and 2011 — that she'd never won a major, unlike Williams' current 23.
Nadal reached the fourth round in Australia for the 11th time with the 6-1, 6-3, 6-1 win, and leveled his career head-to-head record with Dzumhur.
Bopanna and Roger-Vasselin will have to be at the top of their game in the next round as they will be up against seventh seeds Mate Pavic of Croatia and Oliver Marach of Austria.
Svitolina, the only seeded player still in contention in her quarter, had five aces, only 11 unforced errors and didn't serve a double fault in the 59-minute match.
The 10-year commitment is also far longer than the WTA has signed in previous host cities, another potential issue if attendance figures don't reach initial expectations.
Federer, the defending champion, finished off a 6-4, 6-4, 7-6 (4) win over Jan-Lennard Struff a half-hour before midnight.
Federer will next face Frenchman Richard Gasquet in the round of 32 on Saturday.
Matches weren't halted Thursday as the highs stayed just below 40 Celsius for much of the day, but that doesn't mean the heat didn't cause issues for the players.
Stan Wawrinka never looked capable of winning his third-round match, losing 6-2, 6-1, 6-4 to American Tennys Sandgren.
Maria Sharapova hurried through the first set on Rod Laver Arena in 23 minutes before beating No. 14-seeded Anastasija Sevastova 6-1, 7-6 (4).
Novak Djokovic beat Gael Monfils for the 15th consecutive time - 4-6, 6-3, 6-1, 6-3 in temperatures that reached 40 degrees Celsius.
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