NEW YORK, NY, USA - Former World No.1 Naomi Osaka continued her quest for a second US Open title, dispatching No.14 seed Anett Kontaveit, 6-3, 6-4 to reach the quarterfinals in Flushing Meadows for the second time in three years.

"I thought it was pretty good," Osaka said of her on-court composure. "If I'm reflecting on attitude, I'm pretty sure it was up there with my top matches of this short year."

Facing an opponent who pushed her to three sets just last week, Osaka, who emerged on-court wearing a mask that paid tribute to Trayvon Martin, made it through the match without facing a break point to advance in 72 minutes under the lights of Arthur Ashe Stadium.

"It's quite easy to get down on yourself, especially when you feel like you could have already converted so many opportunities, but I just told myself that she's a great player who's supposed to hold her serve, so just to keep pushing."

Though Osaka had never lost to Kontaveit in four previous matches, their most recent clash had come at this very venue last week at the Western & Southern Open, where the two-time Grand Slam champion rallied from a set down to win a hard-fought thriller. After coming from a set down to defeat 2019 Australian Open semifinalist Danielle Collins, Kontaveit hadn't lost another set in her search for a second Grand Slam quarterfinal of the season, having become the first Estonian to achieve the feat in Melbourne back in January.

Osaka twice recovered from second-set lulls against Misaki Doi and Ukrainian teen Marta Kostyuk to reach a third straight US Open second week, and was on a roll after winning the final five games against Kostyuk.

Opening the match with a break of serve, the former World No.1 dropped just six points behind her own delivery as she edged ahead 5-3, stepping in on crucial returns to overpower the Estonian and take the first set.

"My leg felt better today," she noted during her on-court interview when asked about the left hamstring injury that forced her to withdraw from the Western & Southern Open final last week. "I was moving quite well, so I'm very happy about that."

Kontaveit, who was ranked as high as World No.14 last spring, steadied early in the second, staving off a break point to keep on more even footing with her Japanese rival, but struggled to make inroads on return, winning just three of Osaka's first 23 service points in the second set.

Saving two more break points in the sixth game, Kontaveit looked to level the set as she served to stay in the match. What followed was a marathon that featured six deuces and five saved match points. The sixth concluded after a brutal rally on which Kontaveit blinked, netting a forehand beneath the weight of Osaka's impressive pace.

In all, Osaka played a clean match, striking 21 winners to 18 unforced errors while losing just five points behind her first serve. While Kontaveit made 16 winners of her own, she also made 22 unforced errors and couldn't manage a break point opportunity through two sets.

Up next for Osaka is American Shelby Rogers, who booked her second career Grand Slam quarterfinal earlier in the day with a dramatic win over two-time Wimbledon winner Petra Kvitova, saving four match points to survive a final set tie-break.

"I haven't played her in a while, but she's a great player. I'm just going in there very optimistic. I might be the underdog because I've never beaten her. I'm just happy to still be here."

Osaka and Rogers' only tour-level match was back in 2017, where the South Carolina native ousted Osaka to reach the quarterfinals of the Volvo Car Open in Charleston.

2020 US Open highlights: Osaka conquers Kontaveit