NEW YORK -- Before dissecting her 6-4, 6-3 quarterfinal win over No. 8 Karolina Pliskova on Tuesday night, let's pause for a moment to breathe in what Serena Williams has accomplished in the past five days in Flushing Meadows.

She handed her sister, Venus, the most lopsided loss of her season, survived a three-setter against a giant-killer who'd already unseated the No. 1 player in the world and overcame early-match jitters to beat a top-10 opponent for the first time since returning from maternity leave to secure a spot in the US Open semifinals for the 12th time in her career. In other words: It's time to stop hedging predictions and start expecting Williams to win this tournament and tie Margaret Court's all-time record for major wins.

"Serena's one of the best players in the world," Pliskova said after the match. "Doesn't matter that she's No. 17 or 18 now. I think she's still the strongest. I feel like she has a big chance because the players which stayed [in the tournament], I feel like she can beat all of them."

Coming into this tournament, Williams had won only one match on hard courts since she made the final at Wimbledon, and in San Jose in late July, she suffered the most lopsided loss of her career, a 6-1, 6-0 drubbing by unseeded Johanna Konta of Great Britain. Aside from Williams' coach, Patrick Mouratoglou, who has been saying since her first match at Indian Wells that she will win a Slam this season, no one was making bold predictions for her play in New York.

Even Williams, from the moment she returned, has downplayed her expectations and assessed each win as little more than a surprise bonus step on a long road to returning to "Serena" form. Even after an impressive win Tuesday night, Williams refused to fall into the trap of making public predictions about her chances to win a seventh US Open title.

"I'd been a couple steps away at the last Grand Slam, so I'm definitely not ahead of myself," she said. "I still know that no matter whether I'm in the semifinals or the finals, I have a really long way to go to win. That proved to be true at Wimbledon. I'm just taking it one at a time, literally."

One match at a time. One game at a time. One point at a time. That was the blueprint Williams followed Tuesday to fight her way back from down 3-1 in the first set and save three break points to take the game and keep fighting. Slowly, point by point, Williams relaxed, started to better predict and return Pliskova's powerful serves and began controlling points and winning games.

Serena Williams beat a top-10 opponent for the first time since returning from maternity leave. Robert Deutsch-USA TODAY Sports

"I just thought that I wasn't playing my best tennis," Williams said. "I was thinking, 'I can play better.' So that was the good news. Then I thought, 'Just try to make less errors.' Because at that point, I was missing a lot of shots. I just had to figure out a way to try to at least make one and one at a time."

By the start of the second set, Williams had more than filled in the holes in her game. She struck three aces in her first two service games and was quickly up two breaks on Pliskova. After being down 3-1 and facing seven break points, Williams had won eight straight games.

"In the beginning, maybe she was a little bit nervous," Pliskova said. "I know she can be off. She can make mistakes. She can also quickly be back in the match with a couple games or couple shots. She can hit unbelievable shots."

But even when a sprint to the net ended in a beauty of a drop shot that brought her coach, Mouratoglou, to his feet, Williams was subdued in her reactions. There were no fist pumps, no Serena screams, no yells to herself to, "C'mon!" She was as calm on court as she has been all tournament, channeling her emotions into making masterful shots.