AS SERENA WILLIAMS made her way out to the Australian Open’s main court during pre-match introductions, the voice booming over the stadium’s speakers implored spectators to welcome “the world’s No 1 player — from Romania, Simona Halep.”

Oops.

Williams, wearing headphones, quickly pivoted and retreated back into the tunnel she’d just emerged from, making way for her fourth-round opponent last night. A couple of hours later, when Williams wrapped up her 6-1 4-6 6-4 victory over Halep in a contest filled with momentum swings and fantastic play by both, it was clear which woman really is No 1, regardless of what the current rankings say.

“It was a really intense match, and it was some incredible points,” said Williams, who improved to 9-1 against Halep and now meets 2016 US Open runner-up Karolina Pliskova in the quarter-finals. “I love playing tennis and I love to play here and I love to be back out here.”

The 37-year-old sat out last year’s Australian Open after giving birth to a daughter months earlier and dealing with health complications. Since returning to the tour, Williams has reached the past two grand slam finals, losing both — and leaving her still one shy of equalling Margaret Court’s record of 24 major singles titles.

Halep offered up the first real test Williams has faced at this year’s Australian Open, where she is bidding for an eighth trophy, pushing her throughout a back-and-forth match-up that was a fascinating mix of power, court coverage and shotmaking.

It wasn’t until Williams saved three break points in a monumental game to hold for three-all in the third set that she gained control. She then broke for a 4-3 lead and finally was on her way.

“In order for me to stay out there, I had to play a little like I knew I could,” said Williams, who is seeded 16th on account of all the time she took away from tennis while becoming a mother. “I’m such a fighter. I just never give up. It’s definitely something that’s innate. I just work so hard for every point.”