* Osaka backs up her favourite status with 6-3, 6-4 win * American Jennifer Brady beats Yulia Putintseva 6-3, 6-2Naomi Osaka continued to underscore her status as the favourite to win the US Open title as she won her ninth consecutive match since the tour restart, moving into the semi-final with a 6-3, 6-4 win over Shelby Rogers.“I feel pretty good,” Osaka said afterwards. “I think all of the matches were really tough. The scoreline might not suggest it but I’ve had a couple of really hard matches. I think that made me really glad to be in this position right now.”Osaka entered the court wearing a mask bearing the name of George Floyd, whose killing at the hands of police was the catalyst for her activism. She had previously amplified the names of Elijah McClain, Ahmaud Arbery, Trayvon Martin and Breonna Taylor, all high profile cases of Black people unjustly killed at the hands of police or civilians. After the match, ESPN broadcasted messages from Arbery’s father and Martin’s mother for Osaka.“I was just trying really hard not to cry,” said Osaka. “For me it’s a bit surreal. It’s extremely touching that they would feel touched by what I’m doing. For me, I feel like what I’ve doing is nothing. It’s a speck of what I could be doing. It was really emotional. I feel like, I don’t know, after I saw it, at first I was a bit in shock. Now that I’m here and I took the time, I don’t know, I’m really grateful and I’m really humbled.”Despite sporting tape across her left hamstring after her withdrawal from the Western & Southern Open final two days before the US Open began, Osaka is playing some of the best tennis of her career in New York.Rogers, a lovely ballstriker who reached the quarter-finals after saving four match points against sixth seed Petra Kvitova, was rendered impotent by Osaka’s combined package of elite serving power, athleticism and an evolving understanding of how to use her strengths. Osaka ended her night with 24 winners and just eight unforced errors. Despite some struggles with her ball toss, she won a handsome 83% of points behind her first serve.The win marks Osaka’s third career grand slam semi-final, a reminder of both her relative inexperience on this stage but also how dangerous she is when she hits top form. In her two previous forays past the fourth round – at the 2018 US Open and 2019 Australian Open – she carried her momentum to back-to-back titles.In the semi-final, Osaka will face Jennifer Brady. No player at the top of the sport has improved this year as much as the American, who earlier took a major step forward in her career, outplaying Yulia Putintseva 6-3, 6-2 to reach her first US Open semi-final without dropping a set.Although Brady may be unknown to the world beyond the tight circle of dedicated tennis fans, none of this is a surprise. She started the year with wins against the No 1 Ashleigh Barty, Elina Svitolina and Maria Sharapova. In her first tournament after the tour suspension last month, she won her first WTA title in Lexington without dropping a set. Her run through the first five rounds of the US Open has been a simple, brutal continuation of her form.Across the net on Arthur Ashe Stadium, Putintseva is notoriously volatile in her attitude and temperament, but at 5ft 4in she prides herself on outsmarting her opponents with her deep toolbox of shots. Throughout the match, she was simply overwhelmed by the quality that Brady brought to each point.Brady started the match bullying Putintseva with her serve and forehand, and she held for a quick 3-0 lead with three aces. When the Kazakh attempted to change up the match with a drop shot at break point down, Brady ate up the ground and landed a delicate angled forehand before holding to lead 4-0. Brady cooled down as the first set wore on, losing one of her breaks, but navigated through to a 6-3 win.Putintseva attempted to throw off Brady’s rhythm by varying her shots and lengthening the rallies in the second set, but she was only successful for a two-game interlude when Brady lost consecutive games from 2-0 to 2-2after a series of backhand errors.Brady responded with an incredible return game, immediately breaking back for 3-2 in the second set. Despite staring down the prospect of a first slam semi-final, her nerves never betrayed her. She served brilliantly until the end.Until this year, Brady’s career high ranking was 55th and she dipped in and out of the top 100. Her rise further shows that not everyone bursts through as a wide-eyed teenager ready to take on the world. There are so many talented players yet to find the correct conditions to thrive. Finally, Brady has found hers and now she is a clear contender for her first slam title.