Halep opened with a break of serve, but that was as good as things got for the top seed in the first set as Williams came storming back by winning the next six games in a row to take it in just 20 minutes.
The victory was a major step towards the 37-year-old USA great equaling Australian Margaret Court's all-time record of 24 Grand Slam wins as she powered into the last eight.
After surrendering serve for the fourth time in five service games, the Romanian trailed 6-4, 2-1 before sealing her first break of the match, and hung with the 23-time major champion through the duration of the middle set before sealing it with back-to-back games of her own.
Williams, searching for her first Grand Slam title since coming back from pregnancy past year, has now won nine of her 10 meetings with Halep.
The American, who won the title when pregnant on her last visit down under in 2017, was forced to work far harder than in her first three matches at Melbourne Park as the Romanian fought back in the second set, but the American regained her composure to advance to the final eight.
Former world number one Serena Williams has survived a nerve-wracking three-set thriller to book a spot in the Australian Open quarterfinals beating current no. 1 and first seed Simona Halep of Romania 6-1, 4-6, 6-4.
Williams will face Karolina Pliskova in the quarters after the Czech seventh seed eliminated Garbine Muguruza in straight sets earlier on Monday.
Serena faces toughest test since return against Halep
Asked about the incident, Williams said: "As she was walking towards the net, I could tell she was quite upset". "I liked that. She will face the victor of older sister Venus and top seed Simona Halep for a place in the quarter-finals.
"She's the number one player in the world and there's a reason why.in order to stay out there I had to play a little bit like I knew I could".
Williams denied her win over the world number one after not playing since September was a poor reflection on the state of women's tennis. She's a great player. I just never give up. She then broke for a 4-3 lead and finally was on her way.
If Williams goes on to extend her record victories in Melbourne, she will equal Australian Margaret Court's all-time tally of 24 Grand Slam titles. I don't know, it's definitely something that's innate.
She put the minor statistical setback behind her in a strong finish, and said later, "Technically I'm supposed to be good at starting matches".
Against Halep - who beat Serena's older sister, Venus, in the third round - Williams frequently pumped her fists or yelled "Come on!" after key exchanges.
That she does. She also makes abundantly clear just how much every point means to her.