The 25-year-old Greek, who won the title in 2021 and 2022, kept his cool after a near-flawless display in the opening set to stop Sinner from producing a stirring comeback after the Italian roared back to take a 3-0 lead in the second set.
Sinner continued to build momentum after levelling things up and raced to a 4-3 lead in the decider before an injury on his right leg forced him to take a medical timeout.
The 22-year-old Italian continued the match but proved no match for Tsitsipas who re-asserted himself to win three games in a row and clinched the match.
"It was tennis at the highest level that I have been able to play," Tsitsipas said after the match.
"He is one of the toughest opponents I have faced so far... to find a way when there were not many, I am extremely proud of that."
Sinner had been in red-hot form this year, having won the Australian, Rotterdam and Miami Open, with his only loss in 23 matches coming against twice Grand Slam champion Carlos Alcaraz in the semi-final of the Indian Wells last month.
Having come into the contest with an 11-6 win-loss record for 2024, the win against Sinner ensured that Tsitsipas returned to the top 10 in rankings after dropping out for the first time since 2019 earlier in the year.
Tsitsipas will either face top seed Novak Djokovic or Norwegian Casper Ruud, who play in the semis later on Saturday.
