By SABC Sport
29th May 2023
The 2021 finalist seemed to have the contest well under control after a slow start when he moved two sets ahead of his Czech opponent but Vesely took the third and had three set points at 6-3 in the fourth-set tie-break to force a decider.
Fifth seed Tsitsipas saved all of them, though, before clinching a 7-5 6-3 4-6 7-6(7) victory and roaring with relief.
The Greek knows he will need to play better going forward, saying: "It was a great comeback from me on that tie-breaker. I didn't really play the way I wanted to play.
"I started just going more to the ball, being much more aggressive on my shot-making, and I kind of dictated a little bit better. The match was very inconsistent from my side. I felt like I haven't played a match with so much inconsistency in a very long time.
"There weren't a lot of rallies in play. He was serving big, so I had to find ways to change that. At times I felt like my footwork was lousy.
"But otherwise I'm happy with how things turned around, and my fighting spirit went on full display in those last few points of the tie-breaker. It was a great way to end it by just being patient and waiting for that chance to pop up."
Tsitsipas has had an up-and-down season so far and struggled with injury after reaching his second grand slam final at the Australian Open but the clay-court swing has seen him find more consistency.
The 24-year-old revealed he is trying to play with a smile on his face having been influenced by Carlos Alcaraz's positive attitude.
"I had a practice session with Carlitos the other day and did throw in a 'thank you' just randomly, and I don't know if he understood that or not," said Tsitsipas.
"I owe a lot to Carlitos because he's such a breath of fresh air. He's so competitive and he's always with a smile on his face, and so much charisma to him and so much positive energy that he distributes.
"I think that's contributed a lot to his growth as a tennis player and his consistency, too. I admire him for who he is. I have that capacity of being that person. I truly believe that."
Eleventh seed Karen Khachanov, who has reached the semi-finals at the last two grand slams, had to fight back from two sets down to beat Constant Lestienne, and the vocal French crowd, 3-6 1-6 6-2 6-1 6-3.
Hubert Hurkacz also survived a five-setter against David Goffin while 24th seed Sebastian Korda saw off fellow American Mackenzie McDonald 6-4 7-5 6-4.