After losing the first two sets, Tsitsipas rebounded to take a 5-7 4-6 6-2 6-3 6-2 victory and progress to the second round of the French Open.
It marked Musetti's second brush with instigating a major upset at the French Open. In the fourth round last year, he took a two-set lead against Novak Djokovic before retiring injured in the fifth.
The match opened as it would eventually end -- with Tsitsipas in complete control. He raced to a 4-1 lead in the first set and even had two break points for 5-1 but Musetti held, broke in return and leveled the set at 4-4.
After trailing 4-5, Musetti then embarked on a seven-game win streak to take the first set 7-5 and grab control of the second set too.
At the other end of the court, Tsitsipas struggled to build any momentum as he made 16 forehand unforced errors in the first two sets.
In the third set, however, the match turned on its head. Tsitsipas won 12 of the first 13 points and subsequently cruised to a 6-2 victory.
As Musetti tired and Tsitsipas rallied, the Greek made light work of the final two sets to close out victory.
"My attitude [changed]," Tsitsipas told Eurosport after the game.
"I wasn't feeling very good in the first two sets, something was off with my game, but Lorenzo played really well, he wasn't giving me rhythm.
"For sure, very happy that things ended that way. Things weren't easy for me in the first two sets but positive, good effort at the end."
Tsitsipas will face Czech qualifier Zdenek Kolar in the second round. His side of the draw is free of Rafael Nadal, Novak Djokovic, Carlos Alcaraz and Alexander Zverev, leaving him a clear run to the final for a chance to better his runner-up finish last year.
Elsewhere in the men's singles, world No. 2 Daniil Medvedev progressed to the second round with a 6-2 6-2 6-2 victory against Facundo Bagnis. Fourteenth seed Denis Shapovalov crashed out, however, following a 6-3 6-1 7-6 (4) defeat to 19-year-old Holger Rune.