A maiden crown in the French capital will return Sinner to number one in the world rankings after current incumbent Carlos Alcaraz suffered a shock early exit at the hands of Cameron Norrie.
The Italian four-time Grand Slam champion is yet to drop a set in the tournament as he hones in on what would be a fifth title of the season.
"Today I felt like first set was very crucial. Francisco is a very talented player it's very difficult to play against him because his level is very high," Sinner said on-court.
"In the second set I raised the level... and I'm very happy to be in the quarter-finals here for the first time."
Sinner edged a close first set, which featured four consecutive breaks, when he pounced on Cerundolo's serve at 6-5 to seize the initiative.
The 24-year-old then immediately stepped up his level in the second set, racing into a 5-1 lead before serving out to book a last-eight meeting with US fifth seed Ben Shelton on Friday.
Shelton beat Russia's Andrey Rublev 7-6(6), 6-3 in the third round to secure his spot, with it being another landmark moment for the 23-year-old this season - following on from his first 1000-level title, won in Toronto this summer - as he will make his debut appearance at the season-ending ATP Finals.
"It's an accumulation of a year's work, a lot of ups-and-downs, great results, poor results and having to bounce back," Shelton said of reaching Turin.
"For me to be able to be in the Finals was a big goal at the beginning of the year."
Race to Turin
Earlier, Bublik downed Fritz 7-6 (5), 6-2 to set up a last eight meeting with Australian world number six Alex De Minaur, who eased past Russian 10th seed Khachanov 6-2, 6-2.
De Minaur has now cemented his place at next month's ATP Finals in Turin, and Bublik still has a chance of reaching Turin himself, albeit a distant one.
The maverick Bublik has been in fine form this week and came from behind in the first-set tiebreak to seal the opener against the world number four Fritz.
Bublik broke the American to move 4-2 ahead in the second set, before again pouncing on Fritz's serve and sealing victory with a winning return.
Despite arguably being in the form of his life in the latter half of 2025, Bublik said it would require a "miracle" for him to win a career-first Masters title in Paris.
"Tennis is very brutal that way, if you have results you're playing your best tennis, if you're not, you're down," the 28-year-old said.
"I have three matches to go, I have to beat the top 10 players, maybe Jannik (Sinner) in the final, so that sounds a bit like a miracle.
"But you never know what's going to happen... it's just focus on the next match and show a good performance."
Canada's Felix Auger-Aliassime booked his place in the quarter-finals as he came from behind for the third time in as many matches in Paris to beat German Daniel Altmaier 3-6, 6-3, 6-2.
The ninth seed is currently one spot outside the last ATP Finals berth, which is occupied by Musetti, who lost on Wednesday to fellow Italian Lorenzo Sonego.
That result, coupled with an Auger-Aliassime run to the title-decider in Paris, would send the 25-year-old above Musetti in the race to the eight-man season-ending showpiece in Turin.
However, before he can think too much about that, Auger-Aliassime must stop the in-form Valentin Vacherot of Monaco.
The Shanghai Masters champion continued his sensational run of form by ousting Carlos Alcaraz's British vanquisher Cameron Norrie in straight sets in the opening match on centre court.