This success has surprised some, and not only because of ill-feeling towards Japan from many Chinese because of the latter's wartime record.
China is not an easy place to work, and, in clothing at least, Chinese consumers tend to revere brands.
But even the label-obsessed need plain bits and bobs for layering or co-ordination.
Chinese consumers are after quality, and UNIQLO's special fabrics, especially its Heattech range for cold weather, function well.
Above all analysts point to the company's savvy Japan-educated Chinese executives who understand both the culture of the Japanese business and that of China.
But the rest of Asia may be harder to crack.
For one thing, a warm climate in several countries means that UNIQLO cannot rely on its cold-weather products as a main driver of sales.
It may have to tweak its formula, which could be risky, says Takahiro Saito, a fashion-retail analyst and author of a book comparing UNIQLO and Zara.
Though they are very different markets, Europe and America offer a cautionary tale.
UNIQLO in America struggled outside the big cities of the east and west coasts.
Growth in the heartlands remains elusive for UNIQLO both there and in Europe.
In part that is because the same business model exists there already with firms such as Gap, says Mr Saito.
But UNIQLO could do better at explaining what it does.
Well thought-out partnerships with ambassadors, such as tennis player Roger Federer,
and collaborations with designers, like Jil Sander, are starting to help.
Mr Yanai, an ardent fan of globalisation unlike many Japanese executives
(the firm's working language is English and many employees, even in Japan, are foreign),
is confident that he can guide UNIQLO through the changes needed.
He also talks of expanding into shoes as well as dresses and skirts, where UNIQLO currently has only slim offerings.
The backlash against globalisation is the biggest risk to UNIQLO's Asian plans, he says.
It could limit free movement of goods and people, disrupting both supply chains and workers.
Still, a Japanese firm that has managed as much foreign success as UNIQLO should be able to cope.