Konta claimed victory in a final-set tiebreak 6-7, 6-3, 7-6 fighting back from 2-5 down in the final set to show her battling qualities.
The number two seed will now take on Marie Bouzkova in the semi-finals with a potential final with Elina Svitolina awaiting and it is a good return to form for the Briton despite the length of the tie.
"I think the scoreline is quite obvious, it was an incredibly tough match," Konta said, after her win. "Very tough conditions out there, it was very windy, very blustery, so it made it extra difficult for both of us to play, really. But I think overall, both of us played at a great level, we played a very exciting match for everybody who was there watching."
"Personally I’m really pleased I’ve been able to come through such a tough match," Konta added. "Especially, it was the first of its kind for me this season, and to be able to come through it, I’m really pleased with it."
"[Potapova] was playing very well, so she deserved to have those match points, and if she was going to win them with a great point, then she was going to win them," Konta said. "That takes nothing away from the quality of match I played."
"I had no reason to doubt I couldn’t stay out there longer, and ask more questions, and maybe set up some more opportunities for myself," Konta added. "That became the case and I’m quite pleased with that."
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