"She played some incredible points on match point, she reminded me a bit of myself," said Williams after the match.
They needed iron willpower to stagger through scrappy quarter-finals on Wednesday and set up a heavyweight meeting in the last four.
Fourth seed Kim Clijsters overcame a late wobble to beat Slovakian Daniela Hantuchova 6-1 7-5 on Monday and set up a mouth-watering Australian Open quarter-final against Martina Hingis.
Lleyton Hewitt was beaten 6-2, 6-2, 5-7, 6-4 by Chilean Fernando Gonzalez in the Australian Open third round.
Second seed Rafael Nadal ground down German Philipp Kohlschreiber to win a tough match 7-5 6-3 4-6 6-2 in the Australian Open second round on Thursday.
Jannik Sinner overcame a debilitating medical episode as well as Dane Holger Rune to reach the quarter-finals of the Australian Open for the third time.
Twelfth seed Patty Schnyder of Switzerland fought back to upset sixth seed Elena Dementieva 6-7, 7-6, 6-2 to reach the quarter-finals.
Andy Roddick and Guillermo Coria raced into the fourth round with crushing victories.
The Wimbledon champion crushed China's Li Na 6-0, 6-2 to become the fifth Russian woman to reach the fourth round.
The top seed began her Australian Open quest with a pulverising 6-0, 6-0 win over 15-year-old Olivia Lukaszewicz on Monday.
Russia's fourth seed Daniil Medvedev crushed Stefanos Tsitsipas in straight sets to set up a title clash with Novak Djokovic at the Australian Open in Melbourne on Friday.
Svitolina wants to give Ukraine a 'little light' after reaching quarter-finals
Rafael Nadal weathered an early serving storm from Kevin Anderson before dismantling the South African giant with a 7-5, 6-1, 6-4 masterclass to reach the quarter-finals of the Australian Open on Sunday.
Check out Aryna Sabalenka's delightful Australian Open trophy photoshoot
Djokovic, seeking a record-extending ninth title in Melbourne, was cruising after winning the opening two sets of his third-round clash but a slip at 1-1 in the third set almost derailed his progress.
World No 1 and top seed Serena Williams was knocked out of the Australian Open by Serbian Ana Ivanovic on Sunday.
Germany's Tommy Haas beat third seed Nikolay Davydenko 6-3, 2-6, 1-6, 6-1, 7-5 to enter the semi-final.
Serena Williams battled her way into the Australian Open semi-finals with a 3-6, 6-2, 8-6 win over Israeli Shahar Peer.
Marcos Baghdatis failed to repeat his heroics of last year and was beaten by Frenchman Gael Monfils in the second round of the Australian Open.
At 27, the second seed is still seeking his first Grand Slam title and hopes to become the first German man to win the Australian Open since Boris Becker in 1996.
Veteran tennis star Leander Paes and his partner Martina Hingis, who won the Australian Open mixed doubles title last month, met India's Prime Minister Narendra Modi, on Thursday.
This milestone underscores his longevity and commitment to the sport, especially considering the physical and mental demands of playing at the top level.
With the victory, Herbert and Mahut added the Melbourne Park title to their US Open, Wimbledon and French Open crowns to complete the career Grand Slam.
Australian Stosur, who has a history of suffering attacks of nerves in front of home fans, struggled to serve out the match at Rod Laver Arena and double-faulted on match point.
Coco Gauff was given a solid workout by former champion Sofia Kenin but continued her lengthy winning streak
Hungarian Timea Babos and France's Kristina Mladenovic defeated Russian duo Ekaterina Makarova and Elena Vesnina 6-4, 6-3 to win the women's doubles title at the Australian Open on Friday.
Karen Khachanov reached the semi-finals of the Australian Open for the first time on Tuesday after ailing American Sebastian Korda retired while trailing 7-6(5), 6-3, 3-0.
Djokovic has never failed to win the tournament after making the semi-finals and he will be heavily favoured to claim a record-extending ninth title at his favourite Slam on Sunday.
Andy Murray embarks on his first Grand Slam campaign as world number one with much stronger title credentials, even if he has lost five finals at Melbourne Park.
On Sunday, Rafael Nadal's extraordinary resilience was on full display as he closed out a marathon five-setter against World No 2 Daniil Medvedev.
IMAGES from the Australian Open matches played at Melbourne Park in Melbourne on Thursday.
From her remarkable comeback through qualifiers to triumphant battles against major champions, Yastremska's resilience radiates on the hallowed Rod Laver Arena.
Jannik Sinner set his sights on mastering clay and grass courts to make himself a complete player
Serena Williams ended the fairytale run of Mirjana Lucic-Baroni at the Australian Open on Thursday with a crushing 6-2, 6-1 win that set up a final against her sister Venus.
Zverev fresh for Australian Open final after being spared gruelling Djokovic test
The Russian, twice a losing finalist at Melbourne Park, went toe-to-toe with the big Pole for almost four energy-sapping hours on Rod Laver Arena
