The world No. 5 won 6-3 6-3 4-6 4-6 6-3 in the semi-final against Zverev at Roland Garros.
After taking a two-set lead, world number 6 Zverev made an emotional comeback to win the third and fourth sets, but after regrouping, Tsitsipas came back strong, winning the deciding set.
Tsitsipas, 22, will now face Rafael Nadal or Novak Djokovic in Sunday’s final.
“All I can think of are my roots, where I’m from, I come from a very small place outside of Athens. My dream was to play here, my dream was to someday play on the big one. Roland Garros scene, I never thought I would, ”Tsitsipas said on court after his victory.
“There were a lot of people today hoisting flags, people cheering me on in Greek, it was very important to have these people around.
“It is very important for me to do my job well enough to be recognized in my country, but not only that, I am very happy that Greece is more of a part of the tennis community now,” Tsitsipas added.
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