The 22-year-old American, ranked 69 in the world, will face eighth seed Klara Koukalova in the last four after seeing off Spaniard Muguruza 7-6 (7-3) 6-1 in an hour and 26 minutes.
Muguruza broke first in the opening set to take a 4-2 lead, but failed to serve out the set as Vandeweghe took the third break point that came her way in the ninth game.
Vandeweghe held her nerve when world number 27 Muguruza earned a set point as she led 6-5, but was thwarted by the New Yorker.
Three mini-breaks in the tie-break were enough for Vandeweghe to take the upper hand and Muguruza was swept aside in the second set as the American fired down five aces to add to her six in the first set and progress in impressive fashion.
Koukalova is the only seed remaining in the tournament after she got the better of Yaroslava Shvedova 6-2 6-4.
The Czech signalled her intent by breaking in the first game of the match and although Shvedova broke back to make it 2-2, Koukalova won the next four games to take the first set.
World number 31 Koukalova wasted no time in taking command of the second set as she raced into a 4-1 lead and sealed her semi-final spot by winning the fifth match point that came her way.
Zheng Jie coasted into the semi-finals by beating Elina Svitolina 6-3 6-0 in just over an hour.
The Chinese will face Magdelena Rybarikova in the last four after a clinical performance against the world number 34 from Ukraine.
Rybarikova moved a step away from the final after beating German Annika Beck 6-2 7-5.