Aussie De Minaur's breakthrough season got even better in the early match, as the 19-year-old defeated Spaniard Jaume Munar 3-4 (5), 4-1, 4-1, 3-4 (4), 4-2.
Top-seeded Tsitsipas had approached the NextGen ATP Finals semis match against Russia's Andrey Rublev in great form.
Tsitispas benefited from the absence of top-seeded, Alexander Zverev who skipped the event to concentrate on the ATP World Tour Finals.
Despite his tender years, De Minaur has already established himself as one of the pluckiest fighters on the ATP Tour, while he boasts breathtaking speed - much like his mentor and two-time Grand Slam champion Lleyton Hewitt.
De Minaur has climbed more than 170 ranking spots since December, up to No. 31.
He said he didn't know how he recovered from those match points.
Chiefs' pass rush rates with anyone, even the Rams
Louis where the franchise was located until 1987. "A little good nugget here and there, but some bad things to clean up". He threw for 249 yards with two touchdowns and no interceptions as he lead Kansas City to a 26-14 win.
"It feels great. I've been playing some great tennis this week here in Milan", Tsitsipas said.
"I've spoken to him (Hewitt) every day, after every match, he sends me a message and we sort of have a little bit of a chat".
"I stayed calm although I had a chance twice to win the match but remained calm".
Three sets on a tie-break, and it was - like, you don't see the difference between the players. Congratulations to Stef and his team for an fantastic year and an incredible week'.
Tsitsipas, who is ranked No. 15 in the world, beat 2017 runner-up Andrey Rublev 4-3 (3), 3-4 (5), 4-0, 2-4, 4-3 (2). I mean, of course both of them playing incredible, but you know what I try to mean.' Does he think it's because of luck?
He said winning the final would be "the cherry on top of an unbelievable season for me".