American
The Pat Cashed-trained Vandeweghe won 6-4 6-1 in an hour and 14 minutes.
She fired five aces and 19 winners to exert her dominance on the clay, despite previously stating her dislike for the surface.
"It's always something special when you beat a world No.1, no matter what stage it is, what venue," Vandeweghe said in quotes published on wtatennis.com.
"To get a victory over a world number one it's a certain pedigree and you definitely hope that you come out at the end with a win.
"I was fortunate enough to be able to do that."
The US Open semi-finalist Vandeweghe raced to a 5-4 lead in the opening set on the back of her strong service game.
The 26-year-old then sealed a decisive break to clinch the first set and gain the upper hand in the contest.
Despite stepping up her attack, Romania's Halep struggled to find a way past her opponent who cruised through the second set to reach the last four of a clay-court tournament for the first time.
Vandeweghe next takes on sixth-seeded Caroline Garcia who overcame Ukrainian third seed Elina Svitolina 6-7 (7-4) 6-4 6-2 in two hours and 16 minutes.
Estonia's Anett Kontaveit advanced with a hard-fought 7-5 6-7 (6-8) 6-4 victory over Russian Anastasia Pavlyuchenkova.
Kontaveit prevailed after 2hr 55min on her fourth match point, when Pavlyuchenkova hit a groundstroke wide.
The final set of the hard-hitting encounter of unseeded players saw breaks of serve in the last seven games.
"The whole match was so close," Kontaveit said.
"I am trying to go for it whatever the score is. I just kept fighting."
On Saturday, Kontaveit will meet Karolina Pliskova who won a tough three-set encounter with French Open champion Jelena Ostapenko.
Czech fifth seed Pliskova came back from dropping the opening set to record a 5-7 7-5 6-4 victory.
