The world number 87, who describes her Wimbledon adventure as a "fairy tale", did not allow the disruption to shake her form or focus and produced a sparkling display of grasscourt tennis to close out the quarter-final against the American.
Rybarikova is the lowest-ranked player for almost a decade to reach the women's last four, where she will face Spain's 14th seed Garbine Muguruza, and the first Slovak to do so.
"I can't believe it," she told the BBC, looking stunned after her victory. "I cannot believe I am a Wimbledon semi-finalist. I need to sleep on it to believe it."
Her quarter-final match started on Court One, but was suspended shortly after 4 pm due to rain, with the score at 2-2 in the second set. With no sign of the weather turning, the match was moved to Centre Court, the only court with a roof.
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Play resumed at about 7.20 pm and 28-year-old Rybarikova raced to the finish line.
The match was a thoroughly entertaining tussle and threw up a rare sight in the women's game -- two players willing to abandon the security of the baseline and charge to the net in the heat of battle. They even used serve-and-volley on occasion.
Big-hitting Vandeweghe's downfall was the careless mistakes that beset her game throughout, leaving her increasingly frustrated. The 25-year-old American, seeded 24, notched up 30 unforced errors compared with her opponent's eight, and double-faulted several times on crucial points.
It has been a dream run for Rybarikova, who was out of action for the second half of 2016 due to wrist and knee surgery. The last time a woman ranked lower reached a Wimbledon semi-final was in 2008 -- China's Zheng Jie, ranked 133.
(Reporting by Pravin Char; Editing by Ken Ferris)
