Williams defeated Halep 6-1, 4-6, 6-4 to reach the quarter-finals of the Australian Open.
The Romanian broke Williams' serve in the first game but that was the only one she managed for the rest of the opening set as the American bulldozed her way through the set in 20 minutes, serving it out with an ace.
Halep lifted in the second set, working Williams around the court and roaring and pumping her fists after fighting back to even the ledger. "She's a great player", said Williams.
"I really needed to elevate my game", Williams said. "It's a super pleasure".
"Only in the Grand Slams it's not allowed, I think this needed to be said". She's the number one player in the world for a reason.
"I've got to return a little bit better the next day that we play, but I will be ready. There's definitely something that's innate". "So I didn't answer the question exactly but that's my feeling". You have to bring it every single point, every single game, until the match is literally over.
However, she has tripped up early twice now, dropping the first set to Su-Wei Hsieh in round three and doing the same on Monday against the stubborn Latvian.
Others suggested that it was rather weird not to at least stand up and applaud her daughter after becoming the oldest player to defeat the world number one at a Grand Slam at 37, and remaining on course for a record-equaling 24th major.
The seven-time champion will meet Czech seventh seed Karolina Pliskova, who beat Spain's two-time Grand Slam victor Garbine Muguruza earlier on Monday, in the last eight.
Nicolás Pereira and Stephanie Brantz discuss how far Serena Williams can go at the Australian Open following her three-set victory over World No.1 Simona Halep. With her supreme endurance and retrieving skills, she started to make a match out of it, staying in the point, returning with interest and forcing Serena to make errors.
As the master of ceremonies in the Rod Laver Arena announced the entrance of "the world No 1 from.", out walked Serena Williams. If it's not too obvious the Chair Umpire lets it happen, and if it becomes too obvious, in general, he tells the player, "please tell your coach to slow down otherwise I am going to have to warn you".
The seventh seed is also her next opponent in Melbourne, but given how she fought it out against Halep, there is a good chance that she can clear the field as she moves to another Major, which will also give her the all-time record for most Grand Slams.
"I felt like I was hit by the train", Halep said after the match.