NEW YORK -- There's no crowd at the US Open this year to pull for Serena Williams and try to push her to victory, so she provided her own encouragement in a tough fourth-round match Monday.

Shouting at herself point after point, Williams came back from a third-set deficit against a woman she lost to less than two weeks ago, and took another step closer to Grand Slam title No. 24 by beating Maria Sakkari 6-3, 6-7 (6), 6-3 at Flushing Meadows.

Williams reached the quarterfinals for a 12th consecutive US Open.

When the match ended, Williams turned and yelled toward her husband, who stood at his front-row seat and yelled right back.

How tight was this contest? The 15th-seeded Sakkari -- who was trying to become the first Greek woman to reach a major quarterfinal -- hit more aces than Williams, 13-12, and more total winners, 35-30.

It was a rematch from Aug. 25, when Williams faded after building a lead and lost in three sets to Sakkari at the Western & Southern Open, a hard-court tournament usually held in Ohio but moved to the US Open site as part of a two-tournament "controlled environment" without spectators amid the coronavirus pandemic.

"Of course I thought about [the loss], but ever so little, because it's a completely different match, completely different scenario, completely different moment," Williams said.

In the earlier one, Williams' legs were cramping by the end, and she blamed herself for that situation, memorably declaring: "I put myself in a bad situation. It's like dating a guy that you know sucks."

That setback made the American 3-2 since tennis returned from its COVID-19 hiatus, all three-setters. And since? She is 4-0 at the US Open.

Williams was two points from the victory at 6-all in the second-set tiebreaker. That's when everything got complicated.

She sent a backhand return long to give Sakkari her fifth set point, then pushed a forehand out.

With that, the set finally belonged to Sakkari, who shook her right fist. She retained the momentum, nosing ahead in the third set by breaking in its opening game when Williams sailed a backhand long. Soon it was 2-0 for Sakkari.

But Williams is rarely one to go quietly, and she certainly did not go quietly Monday.

She smacked a crosscourt forehand winner to get the break back as part of a three-game run, and soon enough Williams had taken six of the last seven games.

Williams, who turns 39 on Sept. 26, will face an unseeded opponent -- either Alize Cornet or Tsvetana Pironkova -- for a semifinal berth.

Williams first won the title in New York in 1999 as a teenager and has six trophies here. In her most recent 11 trips to Flushing Meadows, Williams has four championships, three runner-up finishes and three semifinal losses.

She lost in the final in both 2018 and 2019, part of a stretch in which she has been to the title match at four of the past seven Grand Slam tournaments, falling just short of getting that elusive 24th Slam title, which would tie her with Margaret Court for the most in tennis history.

Unlike Court's, all of Williams' major championships have come in the professional era.