'That's definitely a warning to never do that': Naomi Osaka uses Djokovic disqualification to keep her cool in US Open win (VIDEO)

While former champions Novak Djokovic and Angelique Kerber were both dramatically eliminated from the US Open on Sunday, former US Open champion Naomi Osaka stayed on top of her game to progress to the quarterfinals.

Djokovic was thrown out of the tournament after hitting a ball into a line judge's throat, while Kerber was dumped out of the women's draw by American Jennifer Brady.

But on a dramatic day in New York, Osaka had no such problems as she blasted her way past Anett Kontaveit in straight sets, 6-3, 6-4, to reach the last eight of the women's tournament.

Osaka cruised to the first set in just 28 minutes, but her frustrations started to show as she failed to convert five match points, and missed eight out of nine break point opportunities in the second set.

But, after hearing what happened to Djokovic earlier in the day, Osaka was determined not to let her emotions get the better of her.

"I didn't really see what happened live (with Djokovic). I was sleeping because I knew I was going to play a very late match but, yeah I saw it afterwards, the aftermath," she said in an on-court interview.

"For me, that's definitely like a warning to never do that."

Osaka's victory means she'll take on unseeded American Shelby Rogers for a place in the semifinals. Rogers scored a big scalp of her own as she saved four match points before knocking out two-time Wimbledon champion Petra Kvitova 7-6, 3-6, 7-6.

The matchup is made all the more fascinating given the head-to-head record between Osaka and Rogers.

Osaka has lost all three of her prior matches against the American, who also defeated Serena Williams last month. But all three of their previous matches took place before Osaka's rise to the top of the sport, and Osaka admitted that their past matches seemed a lifetime ago.

"I don't know, it feels like such a long time ago. I have to definitely watch a couple more matches of hers," admitted a weary Osaka after her win.

"I think she has a great serve and she's a good returner. But I have to study ... It's late. I don't know what I'm saying any more!"