Michelsen, 20, reached the last 16 of a Masters 1000 for the first time with his second win over a top-10 player in eight attempts.
Michelsen survived nearly 50 unforced errors and converted just two of nine break chances, but it was enough to vanquish Italy's Musetti, a two-time Grand Slam semi-finalist ranked 10th in the world.
"It feels really good," the 26th-ranked Michelsen said.
"I've put in a lot of hard work, and it's paying off a little bit. I was wondering when it would happen, and I guess it is starting to happen right now.
"I returned really well today," he added. "I played offensive tennis and executed really well."
In other early action, 11th-seeded Karen Khachanov rallied to reach the fourth round with a 6-7(6), 6-4, 6-1 victory over American Emilio Nava.
Khachanov booked his second Masters round of 16 this season after Rome in May.