The 20-year-old Tsitsipas, ranked 15th in the world, came through 2-4, 4-1, 4-3 (7/3), 4-3 (7/3) against 19-year-old de Minaur after one hour and 41 minutes for his second title after Stockholm last month.
The win was more good news for de Minaur, who had earlier been crowned the ATP World Tour's Newcomer of the Year.
The second-seeded De Minaur hasn't lost a match in the Milan tournament and saved all five break points on his way to a 3-4 (5) 4-1 4-1 3-4 (4) 4-2 semi-final victory on Friday.
Following Denis Shapovalov's withdrawal, the pair were the top-ranked players at the experimental event in Milan, and their supremacy was evident as they both went unbeaten through the event to reach the final.
After a sizzling week in a breakthrough year, in which he's climbed more than 170 ranking spots since December to No.31, de Minaur said he was just enjoying the moment.
He said he didn't know how he recovered from those match points. "I had a chance twice to win the match, but remained calm".
The round-robin tournament for players aged under 21 years has a shorter format than other tournaments, playing sets of first to four games, with tie breaks at 3-3.
"I had a talk with my coach", explained de Minaur.
"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".
Alex landed a deep forehand in the fifth game to force an error from his rival and take it 4-1, losing just eight points on serve in the last two sets and looking strong to wrap up the win in the fourth set.
'Hopefully I'm going to make the pre-season like I never did before and I can perform well next season and can compete with the top players'.
He defeated Spain's Jaume Munar 4-3 4-3 3-4 4-2, the USA's Frances Tiafoe 4-3 4-3 4-2, and Poland's Hubert Hurkacz 4-1 4-3 4-1 to advance to the semifinals.