Since losing in the opening round of the French Open at the end of May, Halep has won two titles and 14 matches. She had to overcome a few early scares en route to number 14, though, fending off four set points in the opening set before eventually seeing off Babos, 75 61.
"It feels good that I won today and I'm into another semifinal," Halep said. "It was a difficult match and I was a little bit tired.
"She played really well in the first set and then in the second set I was a little bit better at the important points and took my chances well."
In the bottom half of the draw, Yvonne Meusburger caused the week's latest upset by defeating No.4 seed Annika Beck, 64 61. Despite playing catch-up for most of the first set, Meusburger hung onto Beck's coattails and then pinched it with a break in the final game before racing through the second and into the third WTA semifinal of her career.
"I think I played a really good match and it was really my day out there," Meusburger said. "I was playing really aggressive and that helped me a lot. I was going for the lines and trying to create pressure for her and this really worked out well."
In the semifinals, Meusburger will face Chanelle Scheepers, who came from a break down in the final set to defeat Danka Kovinic, 46 60 76(5).
Meusburger has split her four previous career meetings with Scheepers, and enters their latest encounter brimming with confidence.
"I'm really happy to be in the semis here, it's fantastic and I really can't believe it," Meusburger added. "I'm just going to rest and try my best in the semis. It's going to be a tough match and I'm just going to try and fight as hard as I can and hopefully I have a chance to get into the final."