With former rival Andy Murray now in his coaching corner, Djokovic was at his imperious and defiant best, cupping his ear to the crowd after winning big points.
Djokovic was at the centre of a row on Monday after he demanded an apology – and got one – from a local TV presenter for what he called “insulting and offensive comments”.
Spain’s world No 3 Alcaraz will have to wait another year to get a kangaroo tattoo. He had vowed to get one if he won the Australian Open for the first time.
The 21-year-old four-time major champion has still never been beyond the Melbourne Park last eight.
He felt he should have rammed home the advantage when Djokovic was struggling with his movement.
“I’m going to say that was the biggest mistake that I made today,” he said.
Former No 1 Djokovic extended his career advantage over Alcaraz to 5-3, having also beaten him in the Paris Olympics final in their last meeting.
Alcaraz got the better of his rival in the 2023 and 2024 Wimbledon finals.
In hot and windy conditions, Germany’s Zverev defeated the American Tommy Paul 7-6 (7/1), 7-6 (7/0), 2-6, 6-1 to step up his quest to win a Grand Slam for the first time.
The 27 year old lost his cool at one point – because of a feather.
The umpire called for a replay when the feather drifted in front of him as he played a shot at a critical juncture.
“C’mon, that is unbelievable on break point,” he shouted, before taking out his fury on Paul by breaking to love.
World No 1 and defending champion Jannik Sinner plays home hope Alex de Minaur in the quarter-finals on Wednesday, the winner facing American 21st seed Ben Shelton or the unseeded Italian Lorenzo Sonego.
Sabalenka will face Paula Badosa in the last four as the Belarusian bids to win the Australian Open for a third time in a row, something last achieved 26 years ago by Martina Hingis.
The world No 1 kept that dream alive but had to battle for it in beating Russian 27th seed Anastasia Pavlyuchenkova 6-2, 2-6, 6-3 in the wind.
“Honestly I was just praying, trying to put the ball back in these tough conditions,” said Sabalenka.
“I’m just super happy I was able to somehow magically win this match.”
At 33, Pavlyuchenkova had been enjoying a late-career renaissance and was the oldest remaining woman in the draw.
Sabalenka next plays Badosa, the Spanish 11th seed who stunned world No 3 Coco Gauff 7-5, 6-4.
Badosa is into her first Slam semi-final at the age of 27.
“I’m a bit emotional,” said Badosa. “I’m a very emotional person. I wanted to play my best game. I think I did it.”
It capped a remarkable comeback for the Spaniard, who was ranked outside the top 100 a year ago after a stress fracture in her back.
“I mean, a year ago, I was here with my back and I didn’t know if I had to retire from this sport, and now I’m here playing against the best in the world,” said Badosa.
Third-seeded American Gauff, 20, described herself as “disappointed but not completely crushed” after her first defeat of 2025.
On Wednesday, Iga Swiatek will look to continue her march to a first Australian Open title when she faces Emma Navarro.
The winner plays Madison Keys or Elina Svitolina in the last four.
