Serena Williams stayed on course for a 24th grand slam singles title at the Australian Open with victory over world number one Simona Halep in a tremendous battle on Rod Laver Arena.

Halep was in the unusual position of going into the match as the number one seed but also the underdog against a player she had beaten just once in nine previous encounters.

The Romanian, who saw off Venus Williams in the previous round, dug in superbly after losing a one-sided opening set to force a decider, and might well have come out on top had she broken for 4-2.

But Williams saved three break points, broke Halep in the following game and served out a 6-1 4-6 6-4 victory to set up a last-eight meeting with Karolina Pliskova.

Speaking on court, Williams said: "It was a really intense match, some incredible points. I love playing tennis, I love this court and it's really cool to be back out here playing.

"I really needed to elevate my game and there's a reason why. She's a great player. I had to just play a  little bit like I knew I could and I did, and I think hopefully that was the difference. I'm such a fighter, I never give up. There's definitely something that's innate."

For all her impressive achievements since returning from maternity leave, Williams had only beaten one top-10 player and had looked nervous particularly in her two grand slam finals against Angelique Kerber and Naomi Osaka.

After mistakenly coming out onto court ahead of Halep when the players were announced and having to retreat into the tunnel, much to the amusement of her opponent, Williams looked like maybe she would again struggle to play freely as she dropped her opening service game to love.

But the 37-year-old has looked fitter and more assured throughout this tournament and that initial impression was swiftly dispelled as she raced through the rest of the set without losing a game.

Halep did not hold serve until the opening game of the second set and was then broken again as the match threatened to run away with her.

But the Romanian got a foothold just in time, breaking Williams for 2-2 and from there the match changed, with Halep managing to compete with her opponent's power.

Handling Williams' serve, unquestionably the best in the history of the women's game, was another matter, but, when Halep did get her chance at 5-4, she grabbed it.

Halep spoke on the eve of the match about not being intimidated by Williams any more, and it certainly appeared that way as she confidently held serve in the early stages of the decider.

Williams was the player struggling to hold on in the rallies and Halep forced three break points at 3-2 only for her opponent to save them all.

That proved the turning point, with Williams seizing on Halep's serve to break in the next game and producing some of her best tennis of the match to serve it out.