First came a visceral roar. Then a tender hug.

Novak Djokovic's emotions poured out after securing an Australian Open quarter-final victory over Carlos Alcaraz that made a mockery of predictions, logic and expectation.

Exuding joy and relief, Djokovic turned straight to his coach Andy Murray and buried his head in the Briton's chest.

The celebration between the rivals-turned-colleagues came following the biggest success of Murray's shock first coaching job.

"It was kind of a gesture of appreciation and respect for him for the fact that he's out there and he doesn't need to be," said 37-year-old Djokovic, who was born a week after Murray in May 1987.

"He accepted to work with me. He's giving all his support to me, to the whole team, and trying to make it work."

When 24-time major champion Djokovic announced in November he was employing the recently retired Murray as his new coach, it felt like a prank.

But there is nothing more serious for both men than winning tennis matches.

Murray has regularly cut a tense figure during Djokovic's run at Melbourne Park, appearing deep in thought about how he can help the seventh seed land a record 25th Grand Slam title.

His relief at the Serb edging past Alcaraz, 21, showed with a heavy exhale of breath.

Then came the moment when Djokovic, who had battled through an upper left leg injury to beat Spanish third seed Alcaraz, trudged over to hug his fist-pumping coach.

"This was a huge win for all of us - including Andy and myself for the relationship," added Djokovic.

"That's why I went to him because I felt very grateful that he's there."