The No.6-seeded Halep needed exactly an hour to beat Dellacqua, 62 62, holding all eight of her service games and breaking four times. Dellacqua came close to breaking Halep several times - she held 10 break points across several games - but the Australian qualifier never converted on any.
And so, Halep moves through to the semifinals of an event at the Premier Mandatory level or higher for the first time, and there's a cherry on the cake - she's now projected to rise from No.7 in the world to No.6 or No.5, depending on results the rest of the tournament - either would be a new career-high.
"Today was better than the last few matches," Halep said afterwards. "I felt very good on the court. I was moving really well. I had no pressure, and I was more relaxed than I was in yesterday's match.
"My game is to be aggressive and hit the balls, and I did much better than the days before."
Halep was asked to elaborate on why she felt less pressure this time than in her previous matches.
"The last two matches I won were very important," she said. "I said before that in the quarterfinals I'd be able to enjoy it and just do what I could, and that's what I did, and it was going very well."
And how far ahead is she looking? "Winning the tournament is too far," she said. "I have my chance and I'm trying to get it, but the next round will be very tough, so I just have to keep trying my best."
Halep will next face either No.2 seed Agnieszka Radwanska or No.7 seed Jelena Jankovic, who played their quarterfinal match at night. Halep has wins over both of them this year - Jankovic at the Aussie Open, Radwanska in Doha. She was asked about that aforementioned victory over Radwanska.
"It was my best tennis," Halep said. "She had 5-2 and was playing really well. I started the match with one tactic, but it wasn't too good. I wanted to hit every ball, and she likes this game. Then I knew I had to change something. I started opening the court more and using angles. I started finishing the points very quickly - if you stay in the rallies with Radwanska, it's not easy. You really have to run a lot.
"She's a very smart player, and I wanted to play the same as her - that was my tactic after 2-5."
Dellacqua was playing the biggest quarterfinal of her career, having never been this far at a Premier-level event, let alone a Premier Mandatory-level event. She was also the first qualifier to make it to the quarterfinals of the BNP Paribas Open in a decade - Gisela Dulko was the last to do it in 2004.