The 37-year-old American dismantled Halep’s game to race through the opening set in 20 minutes. Romania’s Halep, 27, recovered in the second and broke in the final.
Williams, who was placed in 16th place, saved three decision points for 3-3 in the decision and decisively won the next game to take control.
The 23-time Grand Slam winner held her next serve comfortably on the edge and then came in an hour and 47 minutes to victory over last year’s runner-up.
Triumphantly, the air flapped with both arms as she stared hard at her crate, showing how much she felt when she beat the number one in the world. It was an intense match and there were some incredible points, but I love being here, she said.
Williams, who has been searching for her first Grand Slam title since her last Grand Slam title since her last pregnancy last year, has now won nine out of ten meetings with Halep.
The seven-time champion meets Czech seventh Karolina Pliskova, who defeated two-time Grand Slam winner of Spain, Garbine Muguruza, in the last eight on Monday.
If Williams continues to expand her record number of victories in Melbourne, she will reach the total of the 24 Grand Slam titles of the Australian Margaret Court.
From the moment these two players were drawn in the same section of the Australian Open – and expected to meet in the last 16 days – the tennis fans had a feeling of anticipation: Williams, the longtime former world number one, current holder Halep.
And a match with fight, drama and high quality tennis of both players did not disappoint.
Halep admitted before the game that Williams was still the “best player in the world”, and Williams might have proved it with their first win against a number 1 player since beating Victoria Azarenka in 2013.
“I really had to improve my game,” Williams said. “She’s number one in the world and there’s a reason for that, she’s a great player.”
Williams left the Melbourne team in Melbourne with the ease with which they dismantled Halep’s game, especially the Romanian’s second serve, in a one-sided opening set.
Halep, who had won her first Grand Slam at the French Open last year, broke Williams’ serve in the first game, which he was supposed to love – which included a double point penalty – before the American settled down.
Williams allowed Halep only nine more points on the way to the one-set lead. Based on this evidence, those in Laver who thought the second sentence was a formality could have been forgiven.
Nevertheless, Halep has forced each of her fighting qualities to serve in the second second, reducing the unforeseen mistakes and bringing Williams more success. While the set was still fine, Halep won eight of the last 11 points to force a decider.
That was equally competitive: Halep defended Williams in a long opening game before a sixth, which proved crucial.
Halep took three breakpoints – their first chances in the final set – but a 171 km / h serve in the middle, followed by a weak forehand from the Romanian and another booming serve, saw the chance.
This allowed Williams to take control at the crucial moment. Halep made another unforeseen mistake with a forehand to pass the break.
“I’m such a fighter, I never give up, it’s something that’s innate,” Williams said. “It’s a miracle that I’m here and can do something that I enjoy.”
Williams’ coach Patrick Mouratoglou spoke with reporters about last year’s controversial US Open final after the game against Halep for the first time.
Following her defeat at Naomi Osaka in New York, Williams was fined $ 17,000 (£ 13,100) for violating the Code, which called the referee a “liar” and “thief”.
The American reacted poorly after docking a game for verbal abuse. He had already received a fine for abusing thugs and a code violation for coaching.
Williams seemed particularly concerned that he was trained during the game – he would rather lose than cheat to win – but Mouratoglou later admitted that he had actually trained from the pits, even though Williams had not seen him.
“I was not worried at all,” said the Frenchman. “First of all, I hope that every time a coach gets a code violation for the coaching, he will not get fired, otherwise every two days guys are fired.
“Second, I hope that our seven-year relationship is slightly stronger than that of a referee. “Third, if she had done something – I think that would be an emotional decision and she does not. “She’s way too smart to do that, we’re all human and it’s good, there’s no reason to make a decision that affects your future.”