When Elena Rybakina landed in New York, she could barely walk. She left the city carrying the US Open trophy and the title of world number one. "Some magic is happening," she said, clutching the silverware on Saturday night — and it was hard to argue.

The 27-year-old from Kazakhstan arrived at the final Grand Slam of the year nursing a foot injury she had aggravated in a quarter-final in Cincinnati against Iga Swiatek, little more than a week earlier. An MRI in New York "didn't look that great," and she couldn't walk without pain for days. Playing on could have threatened the rest of her season. But the top ranking was within her grasp, and Rybakina wanted to try.

So her team made a plan. She skipped on-court training for a full week, recovering daily in the gym instead. To "switch the mind," she took trips out for dinner and to the cinema. It worked. She won her first four matches without dropping a set — including beating four-time major winner Naomi Osaka — then outlasted Olympic champion Zheng Qinwen in the quarter-finals, edged third seed Coco Gauff in the semis, and outplayed top seed Aryna Sabalenka in the final, 6-4 5-7 6-2.

The final had an extra layer of meaning: Sabalenka was the very player Rybakina would replace atop the rankings. Rybakina's serve, usually her biggest weapon, misfired early — she landed just 27% of her first serves in the opening set — yet still won the set without facing a break point. Sabalenka levelled the match in the 12th game of the second, but it was Rybakina who dominated the decider. Former British number one Annabel Croft described her as "like a machine," giving no emotion away. The nerves did finally surface as two double faults crept in while she served for the title. At 40-30, trophy in sight, Rybakina could have blinked. Instead she sent down her 12th ace of the match to seal her third Grand Slam title, celebrating with a rare smile and both arms raised.

On Monday, Rybakina becomes the 30th woman to top the world rankings, ending Sabalenka's 99-week reign. Croft believes she has "the right personality to deal with it." Only the French Open now stands between Rybakina and a career Grand Slam — she has won Wimbledon, Melbourne and now New York, though she has never gone past the quarter-finals at Roland Garros. Former player Laura Robson called her "an all-surface player" and said when her serve and return are firing on a hard court, "I just don't see how pretty much anyone can beat her."

"I was so unlucky with the injury, but I'm very proud," Rybakina said. "I still can't believe it."