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.
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.
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.
McDonald broke Dimitrov's serve three times in the fourth set and pushed the fifth beyond 12 games, before his first double-fault of the set suddenly gave Dimitrov a match point. Dimitrov finished it off 4-6, 6-2, 6-4, 0-6, 8-6 to enter the 3rd round
Former Australian junior champion Marta Kostyuk, who entered the season-opening major ranked No. 521, followed up her opening win over 25th-seeded Peng Shuai with a 6-3, 7-5 victory over wild-card entry Olivia Rogowska.
Maria Sharapova said it was her choice to return, though, and she relished every moment of it in Tuesday's 6-1, 6-4 victory over Tatjana Maria.
No. 4-ranked Alexander Zverev said Djokovic did most of the talking at the meeting, which was attended by all of the top male players at the season's first major.
Djokovic tweaked his service motion while recovering from an injured right elbow, and used it to good effect in a 6-1, 6-2, 6-4 win over Donald Young.
Nadal also found his championship form again in a 6-1, 6-1, 6-1 rout of 37-year-old Victor Estrella Burgos in the first round at Melbourne Park.
Yuki Bhambri is yet to win a round in the main draw of a Grand Slam and the Australian Open is the only Major he has played.
Serena Williams' exit followed U.S. Open champion Sloane Stephens' 2-6, 7-6 (2), 6-2 loss to Zhang Shuai.
The 19-time major winner can afford to relax slightly longer, given the half of the draw that he shares with Djokovic doesn't start until day two of the Australian Open.
Bhambri overcame a first set lapse to tame Canadian Peter Polansky 1-6 6-3 6-3 in the third and final qualifying round.
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