Second-seeded Medvedev dispatched the number 19 Italian in 93 minutes with three breaks of serve, pushing his tour-leading number of hardcourt match wins to 31 with just three defeats.
The 2021 Toronto champion is chasing his sixth title of 2023 and his fifth on hardcourt.
There was disappointment, however, for third-seeded Casper Ruud, who came up just short in his bid to battle past Alejandro Davidovich Fokina, who pulled the upset 7-6 (7/4), 4-6, 7-6 (7/4).
World number one Carlos Alcaraz was bidding for a last-eight place later, facing a third-round match with Poland’s Hubert Hurkacz.
Medvedev said that despite the relatively straightforward score, blustery winds gave him some problems against Musetti.
“It was not easy to play, it was not the worst wind but it was changing from fast to slow,” he said.
“You can’t hit full power in those conditions and you don’t know what to expect.
“It was not easy for either of us, but I did enough to win. I missed some shots today, but I had quite a good level and I’m happy about it.”
Norway’s Ruud served for victory against Davidovich Fokina at 5-4 in the third set, but dropped his serve in the clutch moment.
The Spaniard took the set into a tiebreaker and finished off the upset after three hours on court.
“I kept very focused on every point when he served for it,” Davidovich Fokina said. “I told myself to be there, don’t give up.
“It’s very tough to close out such an even match with so many long rallies. When I broke at 5-4 it was a show of power.”
The 37th-ranked Spaniard is into his fourth career quarter-final at the Masters 1000 level, earning his fifth career defeat of a top 10 player.
Ruud saved two match points in the tiebreaker before succumbing to an opponent who finished with 49 winners and 56 unforced errors.
The match was paused for an hour and three-quarter hours in the second set because of rain.
Davidovich Fokina booked a quarter-final clash with American Mackenzie McDonald, who beat Canada’s Milos Raonic 6-3, 6-3.