Vandeweghe faced a 5-2 first set deficit and had a set point against her at 6-5 but rallied for a 7-6(3), 6-1 victory over the seventh-seeded Spaniard.
Not only did Vandeweghe fire 11 aces but she won 31 of her 35 first serve points, an 89% win percentage. That should come as no surprise, considering the American leads the WTA this year in that statistic at 75%.
Koukalova, who won her first WTA title here in 2005, just topped Vandeweghe last week in Birmingham after being down a set and 5-3.
Rybarikova defeated Annika Beck, 6-2, 7-5, the exact same score she beat her by in their one previous encounter in Madrid earlier this year.
"I'm playing well here and am happy to be in the semifinals," Rybarikova said. "I'm looking forward to a good match tomorrow. This is good preparation for Wimbledon."
Up 4-3 against Elina Svitolina, Zheng reeled off eight straight games for a 6-3, 6-0 triumph. The Chinese converted on all six of her break point opportunities and saved four of five on her own serve.