Whenever she reaches this stage of a Grand Slam history tells us that Naomi Osaka always goes on to win it. From the quarter final onwards she simply never looks back.

That impressive feat remains intact for now after the Japanese hero dispatched of a half-fit Karolina Muchova at the US Open on Wednesday night, with a 6-4, 7-6(7-3) straight sets victory sealing her place in the semifinals.

She has endured a rocky few years but Osaka, 27, finally appears to be hitting her stride again. This battle with Muchova, who has been struggling with a thigh problem of late, was as high-level as they come despite the 29-year-old Czech player’s injury, with the brilliance of both dazzling the Arthur Ashe crowd throughout.

From as early as 3-3 in the first set, it was clear we would likely be going to the wire here as the in-form pair barely put a foot wrong while each managing to hold their serve. They did so all the way until Osaka led 5-4. Then Muchova’s nerve slipped at the most unfortunate of times.

The No 11 seed had only committed three unforced errors up to this point, yet in what proved the last game of the set she added one more to help Osaka on her way to the first break and first set of the match.

A frustrated Muchova headed down the tunnel to seemingly treat her thigh and regroup. She took her sweet time on a medical timeout and then returned like a woman on a mission, instantly breaking Osaka for the first time after an incredible forehand winner right on the tramline had set up break point.

Naomi Osaka is into the US Open semifinals after getting past an injured Karolina Muchova

Naomi Osaka is into the US Open semifinals after getting past an injured Karolina Muchova

The Japanese hero produced another impressive display to come out on top 6-4, 7-6

The Japanese hero produced another impressive display to come out on top 6-4, 7-6

Yet the chance to gain some momentum and breathing space in the set quickly evaporated for her, with Naomi immediately firing back in devastating fashion. The four-time Grand Slam champion, sparkling in a glamorous violet dress, was in full flow once more, ripping lethal winners on forehand and backhand as she swiftly cancelled out the early break. There was a feeling that Muchova would come to rue not doubling her lead, which ultimately proved correct.

Still, the outstanding technical quality at both ends of the court was clear for all to see. At 2-2 in the second set, Osaka unleashed a crisp backhand that left her opponent with no chance. Muchova then answered in the very next point with an explosive forearm that had the same result.

Then, having both continued to hold serve up until 4-4, an inch-perfect Muchova backhand landed right in the corner of the court and left Osaka rooted to the spot. The latter hit back with yet another lightning-bolt groundstroke, though it was soon followed by the narrowest of wide shots and a gut-wrenching break to leave Muchova serving for the set.

The response from Naomi? An immediate break back without even dropping a point.

If it wasn’t already, the writing seemed to be on the wall from this moment onwards, despite Muchova forcing a tiebreak in the second and final set of the match. 

Osaka quickly took control of that tiebreak and won it 7-3 to get over the line, ensuring she will meet American star Amanda Anisimova in Thursday’s semifinals.

In her second full season back on the court, having not featured in 2023 after giving birth to her first child, the two-time US Open champion is back in her groove at last. 

This is the furthest she has made it at a Grand Slam since winning the Australian Open in 2021. It’s her best effort at a US Open since she did the same there a year earlier. 

Muchova was not fully fit on the night after suffering with a thigh problem in the lead-up

Muchova was not fully fit on the night after suffering with a thigh problem in the lead-up

But Osaka was still superb at Flushing Meadows as she moved to within one win of the final

But Osaka was still superb at Flushing Meadows as she moved to within one win of the final

The 27-year-old has the opportunity to reach her first Grand Slam final since 2021 on Thursday

The 27-year-old has the opportunity to reach her first Grand Slam final since 2021 on Thursday

For Osaka, it’s very much all or nothing at these major championships. If she doesn’t win them she doesn’t tend to stick around for the long haul. Excluding her four victories, her best finish at a Grand Slam otherwise is the fourth round.

The former world No 1 left fans in attendance at Flushing Meadows purring on Wednesday night, with her electric forearm still a joy to behold despite the wounded foe in front of her.

If she plays with similar aggression and swagger on Thursday, the No 8-ranked Anisimova – who defeated world No 2 Iga Swiatek earlier in the day – will certainly have her work cut out. Brutally, she has less than 24 hours to rest and recover ahead of her most crucial match since 2021.

Nevertheless, a new-and-improved Osaka is simply enjoying the ride in New York.

‘I appreciate the journey a lot more now. I think when I was younger, I kind of just kept thinking the next one, the next one, the next one,’ she explained in her post-match press conference. ‘Obviously I would love to appreciate everything right now, but you know, I have a match to play tomorrow.

‘So yeah, I’ll probably tell you how much I appreciate it at the end of the tournament, which is hopefully on Saturday for me. But regardless, I’m just really grateful to be playing well in this city.’