Musetti, the 15th seed from Tuscany, got off to a flying start to take a 2-0 lead in the first set but then proceeded to lose the next nine games as the Serb, looking confident and sharp, ran away with the game.
Djokovic has won the Miami Open on six occasions but has not featured in the quarters since his last victory here in 2016.
The 37-year-old is now just three wins away from winning his 100th tour-level title.
“He had a really good start of the match. First couple games I started a little bit slow and then I knew that if I give him time, he’s going to make his shots,” Djokovic said.
“He loves kind of running around his backhand, hitting forehands. But he is so talented, he can play any shot in the game on any surface,” he said.
“It was tough, particularly in the first seven, eight games of the match. But I think breaking his serve to come back to two-all and break right away at 3-2, it was a momentum shift and I tried to use that,” he added.
Djokovic will face American Sebastian Korda on Wednesday for a place in the semi-finals after the 24th seed beat French veteran Gael Monfils 6-4, 2-6, 6-4 in a rain-affected match.
Korda visibly struggled with his wrist, however, and said after the match that he had been in discomfort with an injury that has caused him trouble in the past.
“It’s pretty painful right now, we’ll see how it goes tomorrow. Will do a lot of work with my physio now, we’ll see how it is tomorrow.
“I haven’t played a lot of tournaments this year. Hopefully I can play some good tennis and see where it takes me,” he said.
Korda later pulled out of his doubles match with partner Jordan Thompson.
Meanwhile, Argentine Francisco Cerundolo upset fifth-seed Casper Ruud 6-4, 6-2 to take his place in the last eight.
Cerundolo, who enjoys plenty of support from South Florida’s large Argentine community, has now reached the last eight in three of his past four appearances at Miami.
Cerundolo failed to make the most of three break points in the opening game but eventually broke through at 3-3, converting his fourth break point of that game.
The 23rd seed, who lost to Carlos Alcaraz in the quarter-finals at Indian Wells, was dominant in the second set, but his victory was postponed by a three-hour, 30-minute rain delay that arrived when he was 5-1 up.
“I’m super happy. It’s always difficult when you’re playing a really good match, controlling the game, and you have to stop for rain,” said Cerundolo.
“It’s not easy, but I was chill and came back to the match confident and played a really good service game. I’m super happy to get back-to-back Masters 1000 quarter-finals in the US, on hard courts. It’s a great achievement,” he said.
Next up for Cerundolo is 14th seed Grigor Dimitrov, who defeated American Brandon Nakashima 6-4, 7-5.
A day after a thrilling three-set win over Brazilian Joao Fonseca, Australia’s Alex de Minaur was eliminated by tenth-seed Italian Matteo Berrettini who triumphed 6-3, 7-6 (9-7).
Berrettini had the chance to close out the match when serving at 6-5 but let three match points slip and the match went into a tie-break.
De Minaur then had a great chance to force a deciding set when he was 6-3 up but was unable to convert the three set points and Berrettini was able to claw back victory.
The Italian will face third-seed Taylor Fritz who progressed with a 6-3, 7-5 win over Australia lucky loser Adam Walton. (AFP)
