Serena Williams has played four Grand Slam finals since her return from maternity break.

Serena Williams had beaten four Top-10 players since, including Naomi Osaka at Toronto and Simona Halep at Melbourne, and lost to five top-10 players, including the two Wimbledon finals.

Serena Williams had beaten the then world No 1 Halep in a gritty three-setter at the 2019 Australian Open too.

So what made the Williams vs Halep quarter-final at the 2021 Australian Open so special? Was it the fact that the last time they met was a one-sided Wimbledon final loss for the American? Was it the quality of the world No 2 opponent?

On paper, it looked like straight-sets, seemingly routine 6-3, 6-3 win. On court, it was one of the best matches Williams has played since her return from maternity break in 2018.

The standout aspect was the manner in which the 39-year-old went about her play during the win. It was not all power and pace but a tactical, tough-it-out win. After a long time, she showed her range, resilience and recalibration skills to win a very challenging match-up.

A lot of the talk around the veteran Down Under has been about her improved fitness. Williams’ long-time coach Patrick Mouratoglou put it plainly saying she was moving better than at any time since giving birth. We saw this already in her last match, a three-set tussle against a red-hot Aryna Sabalenka where she mixed offense with defence to get a gritty win.

This proved to be crucial against a player like Halep, who employs an endurance-based, counter-punching game on most occasions. The Romanian retrieves that extra ball along the baseline and can run her opponents ragged. To engage Williams, who looks to keep her points short, in long, pushing rallies seemed like the perfect gameplan.

Except, it was the opposite. Such was the veteran’s vintage defence that a player 10 years her junior looked deflated. The most standout statistic of the match was that Williams won over double the points Halep did in long rallies (over nine shots.) That’s significant against someone who defends like Halep. Even more so given her serve was not at its best.

The other crucial point in the match was the seventh game of the second set.

The match had started with Williams firing her groundstokes like cannons but Halep broke back and played a clean game. The American constantly built pressure and got the decisive break as a result and served out the first set. The 29-year-old Halep had made just four unforced errors but had only four winners.

But it was in the second set that the action really heated up. For starters, Williams lost her serve with three unforced errors and a double fault in a strange game were Halep had to virtually do nothing to break.

Williams turned to her box with a bemused “What’s happening?” reaction. So often in the recent past, she has lost steam after small moments like this. But she held on as three more consecutive breaks of serve followed with no player able to build momentum. It became a scramble by 3-3 and then came the game of the match.

In a game that stretched to six minutes, Halep went down 0-40 on serve but fought back to stay in it, saving five breakpoints. Williams, though, just refused to lose that game and after a 20-shot rally, got her sixth breakpoint. A small error and a sliver of luck gave her the game. It is no mean feat to outrun, outmuscle and outhit Halep in a long game. Who do they say fortune favours again?

The 39-year-old then closed out the match in straight sets and set up an even more mouth-watering semi-final against Naomi Osaka, a player with whom she shares so much similarity in game style and another opponent who has beaten Williams in a Grand Slam final.

In the 10th seed’s own words, it was the best match she played at the tournament, even better than the battling win over Sabalenka. “Obviously I had to... going up against No. 2 in the world. I knew I had to do better and that’s what I did.”

Halep, who had impressively problem-solved and changed tracks to beat French Open champion Iga Swiatek in the last match, was at the receiving end against a player who made her own adjustments.

“I just realised I was making a lot of unforced errors on those games that I lost,” Serena said after the match. “I knew I had an opportunity to play better. I was like, ‘just stay in there, you can keep going’.”

Staying in there has got Serena Williams back to a place she is familiar with – a Grand Slam semi-final. It will be her 40th Grand Slam semi-final.

Against a player on an unbeaten streak who hasn’t lost a Major semi yet, a whole new test awaits but after a performance as encouraging as this, Williams and her fans certainly won’t be lacking confidence.