Alcaraz fired 42 winners and broke seven times as he made light work of Italian 17th seed Musetti, who had won their only previous encounter last year on clay.
The Spaniard, the reigning US Open champion, has won his past 11 Grand Slam matches and is through to the last eight at Roland Garros for the second year in a row.
“I think I played such a great level, really high quality of shots. I played a really complete match from the first ball until the last and I’m pretty happy to get through this tough round,” said Alcaraz.
“I try not to think about the number one (ranking), the pressure, winning the tournament. I try to put all those thoughts outside my mind and try just to play tennis, to enjoy it and smile all the time.”
The 20-year-old will face either 2021 runner-up Stefanos Tsitsipas or Austrian qualifier Sebastian Ofner in the next round.
Alcaraz improved to 34-3 for the season and is one win away from potentially meeting two-time French Open winner Djokovic in the semi-finals