NEW YORK, NY, USA -- Former World No.1 Serena Williams of the United States kept her quest for a 24th Grand Slam title alive, maneuvering past Estonia's Kaia Kanepi, 6-0, 4-6, 6-3, in a fourth-round battle on Arthur Ashe Stadium at the US Open.

"Fortunately I didn't feel pressure, and I don't really feel pressure, because I'm on this journey of getting back to where I was," Williams told the media, during her post-match press conference. "I'm kind of enjoying that, to be honest."

17th-seeded Williams dominated the opening set but was then drawn into a three-set tussle, before eventually moving past Kanepi after 96 minutes of play. Williams extended her head-to-head record against the Estonian to 5-0, despite dropping her first set against her opponent in their five meetings.

"It wasn't easy, obviously," said six-time US Open champion Williams. "I think one thing [Kanepi] did well was change her strategy, and started doing just a completely different game and gave me a different look to her game."

"I made one or two crucial errors and that cost me the second set, or at least cost me the first game, then she was holding pretty well at that point," Williams continued. "It wasn't like my level went down tremendously. It was one or two points that made a huge difference in that second set."

Kanepi, a former World No.15 who reached the US Open quarterfinals in 2010 and last year, fired 22 winners to 18 unforced errors in the match. But Williams slammed a whopping 46 winners during the encounter, including a staggering 18 aces.

Williams moves into the US Open quarterfinals for the 15th time in her illustrious career, where she will face another big hitter, former World No.1 Karolina Pliskova of the Czech Republic. Pliskova, the 2016 US Open finalist, dispatched Ashleigh Barty in straight sets earlier on Sunday.

Williams and Pliskova have split their two prior meetings, and, in fact, Pliskova is the last person to beat Williams at the US Open, having defeated Williams in the semifinals of the 2016 edition.

"[Pliskova] came out strong and she came out very well," said Serena, when asked about that 2016 US Open match. "I have watched her a great deal since then. I have taken a lot from that match and I think we are in different positions now. It will be an interesting match."

"Obviously her serve, she has a really good forehand," Williams listed as the best parts of Pliskova's game. "In fact, she doesn't do a lot of things bad. Obviously she was No. 1 last year, so she got there for a reason. She has a lot of strong parts to her game."

Williams lost the first point of the match, but after that, she put Kanepi in immediate danger. The American reeled off four straight points and held for 1-0 with a winning drop shot, then broke Kanepi for 2-0 off of a backhand crosscourt winner on her first break point of the match.

The six-time US Open champion continued to dominate in the opening frame with every facet of her game, garnering a double-break advantage for 4-0 before holding at love for 5-0, with three consecutive aces to close out that game.

Williams completed the bagel once Kanepi blasted a forehand miscue into the net on break point, taking the one-set lead after just 18 minutes of play. The American was 8-for-8 on her first serve in the set, and fired 14 winners, including four aces, against a paltry two unforced errors.

But in the second set, Kanepi began to exhibit the world-beating power which brought her to six Grand Slam quarterfinals throughout her injury-hindered career, as well as a win over World No.1 Simona Halep in the first round this week.

The Estonian blasted a clean backhand return winner past Williams to reach break point in the first game of the second set, and converted it to get on the scoreboard and go up an early break.

Kanepi had no problems maintaining that lead up to the middle of the set, holding in her next three service games without facing a break point. She then claimed a stunning second break of the American at 4-2, crushing a forehand winner down the line to reach break point, before Williams double faulted the game away.

The Estonian served for the set at 5-2, but Williams began to reclaim the range on her forehand, and powered winners off of that wing to claim one break back. Nevertheless, Kanepi showed her mettle at 5-4, fending off two break points and powering through to a hold on her third set point.

Williams, however, recovered early in the deciding set, moving through a tough game to hold serve for 1-0 with a backhand crosscourt winner. Williams then achieved a crucial break of the Kanepi serve in the next game by forcing an error with a deep service return, ably racing to 2-0.

Williams needed to stave off one more break point, surviving Kanepi's chance and holding for 3-0. From there, the American was generally untested on serve, and while Kanepi was still firing huge serves and forehands to hold her own service games, she could never approach another break. Finally, Williams held at love for 6-3, ending the hard-hitting affair with a forehand winner past the Estonian.