In the next round, the quarter-finalist from Miami will face the German Alexander Zverev (3rd).
In a match studded with unforced errors (a total of 43 for Sinner and 31 for Rublev), the Russian raced in the lead throughout the first set before offering the break to his opponent on a double fault (5-5).
But he immediately took over the service of the Italian and concluded on his serve.
At the start of the second set, Sinner conceded his service game.
But the match then completely changed and he lined up six games in a row, despite a huge blister in his right big toe which he treated at 2-1.
The Italian thus equalized with one set everywhere on a white service game.
"I tried to find a solution... in large part it was thanks to the support of the public," said Sinner, who compensated for his unforced errors with 40 winners (19 for Rublev).
In the deciding set, the Italian was more incisive when Rublev opened doors for him, especially on the Russian's second serve.
As a symbol, it was on a winning return on a second ball from Rublev that Sinner concluded the game.
He reached the quarter-finals of a Masters 1000 tournament for the third time after Miami last March and in 2021 when he reached the final.
© 2022 AFP