Earlier on day 11 in Melbourne, Jessica Pegula and Elena Rybakina both won in straight sets and will meet for a place in the final.
The 38-year-old Djokovic, chasing an all-time record 25th Grand Slam crown, has the tennis gods smiling on him.
His last-16 opponent Jakub Mensik pulled out without a ball being hit and now Musetti was forced to retire with the Italian leading 6-4, 6-3, 1-3 on Rod Laver Arena.
The fifth-seeded Musetti was well on top when he needed treatment on his upper right leg, and with his movement badly impeded, was forced to throw in the towel.
“I feel really sorry for him, he was the far better player, I was on my way home tonight,” said Djokovic, who had been uncharacteristically error strewn.
“It has happened to me a few times. He was in full control.
“So unfortunate, I don’t what else to say.
“He should have been the winner today no doubt. I am extremely lucky to get through this one today.”
Djokovic has been trying to move past Margaret Court and clinch the landmark 25 since his last major title at the US Open in 2023.
It has proved increasingly difficult with the emergence of Sinner and world number one Carlos Alcaraz.
Djokovic, who needed treatment during the match for a blister, added: “I am going to double my prayers and gratitude tonight to God for giving me this opportunity again.”
Italian second seed Sinner and United States eighth seed Shelton face off in the last match of the day, with Djokovic awaiting in the semi-finals. (AFP)
