After Novak Djokovic clinched a four-set quarterfinal victory over Carlos Alcaraz in the wee hours of Wednesday morning inside Rod Laver Arena at the Australian Open, the 24-time Grand Slam singles champion's first order of business was to celebrate with the coach he hoped, at his hiring, would hellp him do just that..

The Serb sauntered over to the side of the court where his camp was seated, and roared in delight, fist-pumping with both arms before giving his fellow former world No. 1, Andy Murray, a hug and slapping his chest.

The release of the raw emotion Djokovic felt looked spontaneous on the surface. But in reality, it was intentional. Following the match, Djokovic said that the win was just as "huge" for his longtime rival and the pair's budding player-coach dynamic as it was for himself.

Read more: Had Novak Djokovic lost the second set to Carlos Alcaraz, he wasn't sure if he'd continue playing

"It was kind of a gesture of appreciation, respect for him, and the fact that he's out there, and he doesn't need to be," Djokovic said of his fellow former world No. 1. "He accepted to work with me. He's giving all his support to me, to the whole team, and trying to make it work."

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

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Djokovic and Murray made headlines in November when they announced that they'd be working together as player and coach through the Australian Open, and the early returns in Melbourne have been positive. The Scot, known throughout his playing career as a innovative data-driven competitor, has brought some of that acumen into his first coaching gig. Djokovic, also naturally intuitive as an analyst, has been more than open to Murray's feedback..

"I feel more and more connected with Andy every day. We face challenges every single day. People don't see that obviously," Djokovic said. "We try to make the most out of every day and grow together. He's been as committed to my career and this tournament as he can be."

But whatever strategical advice Murray provided ahead of Djokovic's first-ever hard-court Grand Slam match against his younger rival, it was Djokovic who still needed to execute. He did that, largely, flawlessly over the second, third and fourth sets, while also fighting an apparent groin injury.

The victory puts Djokovic through to a semifinal match against No. 2 seed Alexander Zverev, and just two matches away from not only securing his 11th Australian Open title, but Murray's first.