The 24-year-old had made the quarter-finals at each of the other three Grand Slams and completed the set when she beat Maria Sharapova in the fourth round on Monday, while by contrast Halep had achieved her best result at a major by reaching the last eight at Melbourne Park.
"I think it was also important today because I already was on the stage," Cibulkova told reporters. "I already played a couple quarter-finals in the Grand Slams [and] I already did semi-finals in a Grand Slam.
"So that was my experience today. I was ready for it. It was for me like every other match so I didn't take it too serious [and] put myself under pressure.
"I knew I have to be aggressive. Even if you play well, you play fast, she's there at the ball I knew I had to step into the court and play a lot to her weaknesses, use my backhand down the line that she was not expecting, to play some shots. When I play my great tennis, I'm really aggressive, that's what I do the best."
Cibulkova will now face Agnieszka Radwanska in the semi-finals.