Musetti is safely through to the Australian Open second round, Â advancing when ailing Belgian Raphael Collignon quit during the fourth set of Tuesday's encounter on Margaret Court Arena.
Collignon pulled the pin after dropping serve to trail 4-6 7-6 (7-3) 7-5 3-2, handing the fifth-seeded Musetti a path through to a second-round contest with countryman Lorenzo Sonego.
Fellow Italian, dual AO champion Jannik Sinner also had his night match cut short with Frenchman Hugo Gaston retiring after two sets, trailing 6-2 6-1.
Ninth-seeded American Taylor Fritz had a tight tussle for two sets before overcoming another French player Valentin Royer 7-6 (7-5) 5-7 6-1 6-3.
Musetti was relieved to advance after slugging it out for more than three hours before his opponent stopped.
"I struggled a bit on finding the rhythm and I was missing a lot of easy shots and especially with the forehand and the serve at the beginning," he said.
"I had this feeling, then was fighting and especially after a really rough second set, I managed to play really well.
"I increased the level."
De Minaur and Musetti opened the year duelling for the world No.5 ranking before the Italian nabbed it after making the final in Hong Kong, where he also won the doubles title in a real confidence booster ahead of the Open.
"The year started pretty well for me," he said.
"I made two finals - lost one, won one - so we're even.
"Hopefully coming here with my best ranking of course, top five, is a really great achievement for me.
"But I take that as a starting point, not a finishing point."
World No.1 Carlos Alcaraz and the second-ranked two-time defending AO champion Jannik Sinner have won the past eight slams between them, opening up a huge gap over their chasing rivals.
Even world No.3 Alexander Zverev, runner-up last year in straight sets to Sinner, and No.4 Novak Djokovic, a 10-time Open winner, are miles behind the top two in rankings points.
Musetti, though, is intent on bridging the gap and even contending for grand slam spoils this fortnight.
"The ambitions are really, really high," he said.
"So hopefully I'm trying everything to make it happen, to try to go even higher."
Eighth seed Ben Shelton also progressed on Tuesday, blasting a booming, airborne forehand winner on match point to take down French danger man Ugo Humbert 6-3 7-6 (7-2) 7-6 (7-5).
The American let out a primal roar after sealing the deal against the highest-ranked player in the 128-man draw not seeded.
"Obviously I knew coming in on a court like this, anywhere, playing Ugo first round is a tough draw," Shelton said after booking a second-round date with either Australian qualifier Dane Sweeny or veteran Frenchman Gael Monfils.
"But, for me, it was just focusing on the things I've been doing, focusing on the areas that I've been trying to improve and just try to get better as the match went on.
"I felt like I found some of my better tennis later in the match and that's all you can hope for."
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