The 26-year-old was serving for the match at 15-30, 5-2 in the second set ― after cruising to a 6-2 victory in the first set ― when the heavens opened.
Svitolina, the tournament's top seed, was Wang's highest-ranked top 10 scalp this year.
Muguruza was pegged back after winning an opening-set tie-break, but moved three games clear in the decider.
Wang had seemed in complete control during the match, with the under pressure Svitolina committing a string of unforced errors, before the top seeded Ukrainian was saved by the weather.
It is the first semifinal the two-time Grand Slam champion has reached since making the last four of the French Open in May.
"It was very competitive", the 25-year-old.
Kumkhum broke her as she served for the match, levelling the scores at 5-5, before Muguruza finally overcame her opponent, who is ranked 105.
"Yesterday, I felt very confident that I could win the title, but in the morning, I woke up and I felt a bit too nervous", Yastremska said, per the WTA. "After match point I fell on the floor because I felt so relaxed, that was my instinct to go and lie because I needed to put it away, the emotions".
Wang trailed Muguruza 4-1 in the final set, but showed determination to rally to win the almost three-hour encounter.
"The first and second rounds gave me a lot of confidence - that's why today I played really well", Zhang, 29, said.
Svitolina for a spot in the semi-finals competed with the 24-th racket of the world of Wang Qiang, that after the defeat from the Ukrainian in the third round of the US Open had impressive two-month stretch with the title in Guangzhou and semi-finals in Hiroshima, Beijing and Wuhan.
The 2016 Wimbledon girls singles finalist conquered her nerves as she fought back from an early setback to win only her second WTA quarter-final earlier Friday.