World number one Simona remained on course for a first Grand Slam title as she recovered from a set down to beat German 12th seed Angelique Kerber in three sets.
The Romanian defeated Kerber 6-7 (2-7) 6-3 6-2 to setup a semi-final meeting with 2016 champion Garbine Muguruza on Thursday.
Muguruza had earlier beaten Maria Sharapova of Russia 6-2 6-1 on Wednesday.
Sloane Stephens will face Madison Keys in a repeat of the 2017 US Open final in an all-American line-up in the other semi-final on Thursday.
Speaking after the game about her victory, two-time finalist Halep said: “It’s always a tough match when I play against her. After the first set I just stayed strong and didn’t give up.”
“I missed a lot in the beginning. I tried to do too much. I changed the tactics a bit and it worked.” She added.