MELBOURNE, Australia -- The most telling point of Serena Williams' hard-fought win against world No. 1 Simona Halep didn't happen on match point. It came during a grueling 16-point game in the third set.

Down 3-2 and having just saved three break points, Williams was two serves from surviving the toughest game of her tournament. But on the next point, a dramatic 10-shot rally ended with Halep's forehand catching the net and dropping onto Williams' side of the court, pushing the game to a fifth deuce. "That's not fair!" Williams mouthed to her team as Halep politely waved off the point from across the net.

In that moment, it was tough not to think back to Williams' last match of 2018 in the US Open final, when the pressure of not performing up to expectations and the emotion of what she perceived as an unfair slight by the chair umpire sent her into a tailspin. Visibly frustrated, how would she react Monday night, in the heat of a tight three-setter -- the first she'd faced this tournament (and only her fifth since returning from maternity leave last March)?

Answer: By settling herself, smashing a 103 mph ace and then closing out the game with a perfectly placed forehand winner. "In that moment, Simona was playing a bit better than Serena, and the danger was real," Williams' coach, Patrick Mouratoglou, said after the match. "She knew she should not get broken at that time, and she found a way. Then the match changed."

That is the difference between Williams last season and the Williams of 2019. There is no question the 23-time Grand Slam champ is playing more physical tennis than she was four months ago. Against Halep on Monday, Williams, who won the match 6-1, 4-6, 6-4, hit with more power and speed than she did in her 2017 Australian Open final win over big sister Venus, when she was arguably playing the best tennis of her career. Against Halep, Williams' average topspin on her forehands and backhands was 5 mph faster than it was against Venus two years ago.

"I don't know if [tonight's] the best tennis I've played, but that goes to show you that you have to play well for two sets," Williams said after the match. "You can't just play well for one set or six games. You have to bring it every single point, every single game, until the match is literally over. I feel like each day, each match, and each tournament I'm learning something. Today I'm learning that I have to fight for matches."

Serena Williams now has nine career wins against No. 1-ranked players, the most of anyone in the Open era. JEWEL SAMAD/AFP/Getty Images

Monday night, Williams won a mental battle with herself as much as she won a physical battle against Halep -- and while the former might be the difference between making a Grand Slam final and winning one, the latter is nothing to scoff at. Halep is known for being one of the fittest, smartest players on tour. At 5-foot-5 and with a serve that typically tops out around 105 mph, she has to be, especially when facing an opponent with one of the most lethal return games in the sport. "It's tough to see her so close to the baseline [during serves]," Halep said after the match. "You feel the pressure."

Before the match, Halep said if she wanted to beat Williams at her best, she needed to move her around the court and dictate the pace of the game. True to her word, at long rallies, Halep was superb. But Williams' return was unstoppable, as was her play at the net (12-for-14) and her ability to come up with a big serve when she needed it most. (Williams hit nine aces to Halep's two, and won 42 percent of her second serves.) But most importantly, Williams stayed in the points, gave herself opportunities to win and didn't allow her emotions to dictate her play.

"Emotionally, Serena knew this was a match where she had to really step up," Mouratoglou told ESPN.com. "And physically, she had to show her A-game because there were a lot of very long rallies. Physically, emotionally, Serena's much more ready this year. I'm happy she had a tough match tonight. Having a match like that, she will be ready for anything in the next matches."

Her opponents in the next three rounds won't make for an easy path to a record eighth Australian Open title. Williams faces No. 7 Karolina Pliskova, whom she has played only three times in her career (Williams is 2-1), in the quarterfinals on Wednesday before she would take on the winner of a quarterfinal matchup between Naomi Osaka and Elina Svitolina. Australian Ashleigh Barty or No. 8 Petra Kvitova would be her most likely opponents looming in the final.

"I think her chances to win are higher here [in Melbourne] than they were at other Slams last year," Mouratoglou said. "She has four chances this year. I think she is ready to win the four. I'm not saying she will, but she is ready. And when she's ready, she can do anything."