Another straight-sets victory, this time 6-2, 6-4 over Rublev, moved Sinner up to 32 straight wins in the ATP's top-ranked events, one more than the previous record established by Novak Djokovic in 2011.
"I don't play for records, I play just for my own story," said Sinner on court.
"At the same time, it means a lot to me, but tomorrow is another day, another opponent, a different opponent."
Rublev was Sinner's first seeded opponent at this year's tournament in Rome and the world number one made short work of his task in front of a delighted centre court.
On Friday, Sinner could face Daniil Medvedev, winner of the 2023 title at the Foro Italico, with the seventh seed taking on lucky loser Martin Landaluce in the first match of the evening session.
Sinner looks near unbeatable at the moment and with his great rival Carlos Alcaraz out injured, he is the heavy favourite to become the first Italian to win the Rome title in five decades, with a potential career Grand Slam on the cards at the French Open.
Rublev offered little resistance, the Russian dropping his own serve in the first game of both sets to give Sinner a handy leg-up, and committing 28 unforced errors in 18 games.
Sinner, meanwhile, showed flashes of his best tennis but also started to look tired towards the end of the match, visibly touching his left thigh before confidently serving for the match.
"I'm starting to feel that I've been playing a lot, so I need to recover as much as possible because tomorrow wil be very difficult," Sinner later told reporters.
"However it goes it will be a win for me, if I win great but even if things don't go well, that's OK because I'll have a few more days to prepare for Paris, which is my main objective this year."