Del Potro went on to sealed victory on a fifth match point after nearly four and a half hours of action on Court Two.
She will go into the record books as the lowest ranked player - at 181st - to reach a women's semi-final at Wimbledon; yet having dominated the game for so long, she is carrying on where she left off before her maternity break.
"I don't think Kasatkina has been disciplined enough".
"It was really strong and then I needed to ice it!"
"They changed their mind".
"I think everything right now is a little bit of a surprise", she said.
She was, instead, going to employ spectacular defense and solid, steady play, while letting her opponent, Jelena Ostapenko, be the one to determine the outcomes of almost every point.
"It is a great feeling to be in the final and playing on the Centre Court is always a great experience and I am really excited", she told the BBC.More news: Netflix has just become the top Emmy-nominated network
Asked if she had any sympathy for Hsieh at the time, as replays suggested the Taiwan player did deserve to have the point replayed, Cibulkova said: "No". This happened to me so many times that I had exact the same point, and the point was given to the other player. (In) 2014, I played a good tournament. That's why I spoke to the chair umpire. In 2016 I didn't play because of my wrist. I don't feel I have to win this.
But, for the third time in the match, the broken player hit back at once as Cibulkova found her range from the baseline and broke to love. "It was really ridiculous for me". I'm going to practise tomorrow, recover and get ready for the semi-finals'.
She faces Italian world No. 52 Camila Giorgi today for a place in the semi-finals. We both played on a very high level at the end.
"No, I understand. You know, she's a fighter". "This is only my fourth tournament back, so I don't feel pressure. Maybe she's exhausted and she don't see the ball", she said. It is also the first time it has occurred at any grand slam since Steffi Graf and Anke Huber had deep runs at the French Open in 1993. On the grass she's playing even better than on the clay.
Thursday's other semi-final will also feature a German, two-time grand slam champion Angelique Kerber, against 2017 French Open victor Jelena Ostapenko of Latvia. She then breezed past Taylor Townsend 6-0 6-4 to advance to the third round where she beat Australia's Daria Gavrilova 6-3 6-1.
The 21-year-old Latvian former French Open champion looked in trouble with her Belarusian opponent racing into a 5-2 lead after delivering a superb lob. Her sister, Venus, of course.
This semi-final was billed as attack versus defence and it was the solid, reliable manner of Kerber that prevailed as she let an erratic Ostapenko, who was going for winners on nearly every shot, hand her a swathe of free points.