Seventh seed Musetti, playing his first match since retiring in the French Open semi-final against Carlos Alcaraz with a leg injury, never looked settled against the world number 126 and went down 6-2 4-6 7-5 6-1 on a muggy Court Two.
"Really bad day at the office, I came here at the last minute and of course I didn't have much good feelings with my game and honestly the physical side and energy and whatever it takes to play a match like this," he said.
"I was struggling to feel comfortable on the court from the beginning, I was really losing focus and was not really reactive on the ball. Today felt like I had never played on this surface."
The 23-year-old recovered from a slow start to level the match but Basilashvili, a former top-20 player, raised his game at the end of the third set, breaking serve at 5-6 by winning a stunning rally with a volley into the open court.
Musetti's resistance withered in a 23-minute fourth set as the 33-year-old Basilashvili earned his first win in a Grand Slam since reaching the Wimbledon third round in 2022 and the first over a top-10 ranked player in a Grand Slam.
Musetti's limp exit means 10 men's seeds have already fallen before the conclusion of the first round.