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.
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, with one beautiful cross-court drop shot helping him to break Rublev for the fourth time and take a 4-1 lead in the second set, which gave his opponent too much to do.
"I felt like we both didn't play at our best today, but at the same time, you know, the conditions here are very tough," said Sinner of the changeable and windy weather in Rome.
"I tried to adapt myself in the best possible way, and obviously I'm happy."
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.
The 24-year-old will meet Medvedev, tournament winner here in 2023, in the last four after the Russian came through a hugely entertaining match against Spanish lucky loser Landaluce.
After being picked to replace the injured 14th seed Valentin Vacherot, 20-year-old Landaluce had a dream tournament and looked set for his first Masters 1000 semi-final after racing to the first five games on his way to winning the first set.
But Medvedev stemmed the tide and, helped by a short rain interruption, he roared back with some beautiful tennis as the pair went at each other shot for shot before the seventh seed eventually prevailed.