She defeated her American opponent by 4-6 6-4 15-13.
Halep left fans gasping in concern after rolling her ankle during her first-round win over Destanee Ajava, and even Halep admitted after beating Bouchard that she was anxious entering the match.
"I have never played a match like that before where it went so long in the third set. I'm nearly dead", said the Romanian after finally edging across the finish line.
For Davis, as discouraging as it might be to have nothing to show for all that hard work, it was a very good tournament. So I made, like, a commitment to myself before this tournament that I'm going to be my own best friend and just my greatest supporter, and accept all that God has to give me.
"The feeling in my muscles is gone and I don't feel my ankle anymore", she added. But it was nice to be on court.
Davis required a medical timeout at 11-all after telling the chair umpire her toenail had fallen off. The decider would be longer than the first two sets combined.
Roger Federer eased into the second week with a 6-2, 7-5, 6-4 win over Richard Gasquet, and stayed on course for a 20th Grand Slam title.
Halep looked on the verge of a win when she served at 5-4.
The match included 48 games, which ties the most for a women's encounter in Australian Open history, as two of the most diminutive players on tour played out an epic. Wozniacki had to save four break points while serving for the match but clinched it on her fourth match point.
Davis then had treatment on her right foot before saving five more break points in the next game.
"I'm nearly dead", the tenacious Romanian said after the incredible battle, in which Davis lost a toenail and Halep served for the match four times. I think there is quite a few positives to take away from and to learn from, so things are looking up.
It eclipsed the 3hr 1min that fellow Romanian Irina-Camelia Begu took to defeat Ekaterina Makarova of Russian Federation 3-6, 6-4, 8-6 in the first round on Monday. I did that, and I think she was a little bit exhausted at that moment. My ankle, I don't know how it is because I don't feel it any more.
She will next test herself against French eighth seed Garcia, who was too strong for Belarussian Alaksandra Sasnovich, winning in three sets. Incredibly, the Hungarian had not won a Grand Slam match before this year's Australian Open - finally coming of age at 25.
Earlier, sixth seed Karolina Pliskova beat Czech Fed Cup teammate Lucie Safarova 7-6, 7-5 to move into the fourth round.
World No. 1 Simona Halep saved three match points to survive a titanic struggle and make the last 16 at the Australian Open, here on Saturday.
She advances to play either Barbora Strycova or American Bernarda Pera in the fourth round.
More cynical minds see Tebow's invite as a promotional stunt, that will allow the Mets to sell more spring training tickets. The Mets on Friday announced nine players, including Tebow, who have been invited to spring training.
Facebook's letter confirms that the company will begin to look for evidence of meddling beyond the Internet Research Agency. If the company finds evidence of other troll farms, it may prompt US lawmakers to reopen their investigations.
Those two fragments of the market have generally been a little level of Amazon's enormous populace of Prime clients. Amazon said Friday it is raising the fee on the pay-by-the-month version of Prime from $10.99 to $12.99 a month.
At the 2018 North American International Auto Show now underway in Detroit, Ford has made happy campers of many an automotive fan. On Friday, Ford will auction off the 2019 Ford Mustang Bullitt with VIN 001 at Barrett-Jackson's annual Scottsdale Auction.
General Electric slipped 4.5 percent, extending losses from Tuesday, when it announced more than Dollars 11 billion in charges. Industrial stocks rose after the Federal Reserve said USA industrial production increased 0.9% in December.
The story also claims that Roma are likely to demand a transfer fee of around £22m for Emerson this month. Emerson is 23-years-old and has been out of favour this season, making just one Serie A appearance.
Croix County medical examiner since 2011 and has served as a leader on local mental health- and addiction-related initiatives. Sheila Harsdorf held the seat from 2001 until November when she resigned to become Walker's agriculture secretary.
The bureau also said it would grant waivers to companies as the first sets of regulations going into effect later this year. Last week, a federal judge denied a request by English for a preliminary injunction to remove Mulvaney from the job.
Two escorts with the Nigeria Police Force were reportedly killed by the armed kidnappers, before the foreigners were abducted. Victims are usually released after several days once a ransom is paid.
EC disqualifies 20 AAP MLAs over office of profit
The commission has now concluded that the post of parliamentary secretary did indeed qualify as an office of profit. AAP spokesperson Saurabh Bhardwaj said: "Till now, there is no confirmation on the EC's recommendation".
Aussie debutant Carey replaces Paine for second ODI
The Australian scored only seven before popping back a return catch to Root and then bowled seven wicket-less overs for 55 runs. However, when Marsh was stumped by Jos Buttler off the bowling of Adil Rashid for 36, the Australian innings began to falter.
President Trump Makes Decision on Immigration
Asked Tuesday about Trump and some Republicans challenging his honesty, Durbin tells reporters, "Politics ain't beanbag". Trump and his doctor discussed his diet and exercise during last week's physical and set a goal of losing 10-15 pounds.
GST Council slashes rate on 29 items in Budget 2018
The decline in tax collection will amplify the Centre's fiscal concerns ahead of the Union Budget , scheduled for February 1. The meeting also approved a definition for handicrafts and the designation of 40 items as handicrafts.
US marshal shot, killed while serving warrant
The fatal shooting of a USA marshal in Harrisburg hits close to home for law enforcement authorities in Berks County. Frein was subsequently convicted and sentenced to death for killing a state trooper. "He was the cream of the crop".