Jan 17 (Reuters) - Emerging market stocks fell on Tuesday, breaking a 10-day winning run, as weak economic growth in China renewed worries about an economic downturn, while South Africa's rand stabilised following a sharp move lower over power outage worries.

Following a stellar rally, MSCI's index of emerging market shares fell 0.5%, with Hong Kong's main index, which includes heavyweights such as Tencent, Alibaba and Baidu, down 0.8%.

The slide in the broader EM index comes after it gained more than 20% since hitting a 2022 low in October, helped by hopes of an economic recovery in China as it eased COVID-19 curbs, as well as expectations that the U.S. Federal Reserve would opt for smaller interest rate hikes.

But sentiment was dented on Tuesday after data showed China's economic growth in 2022 slumped to one of its worst levels in nearly half a century.

"The current wave of COVID infections is likely to weigh on China's growth at the beginning of this year. But the swift and abrupt reopening means that the time to bottom out will likely to be much shorter too," said Tommy Wu, senior economist at Commerzbank.

"We expect economic activity could return to normal in the second quarter or even as early as March. Moreover, the government's policy support will help to facilitate the recovery."

But China's long-term outlook looked bleak too with data showing China's population fell last year for the first time in six decades.

Several Asian bourses were in the red, as were those in central Europe and South Africa.

Emerging market currencies also looked to have marked an end to a rally that saw an index rise nearly 3% over 15-straight sessions of gains, a streak that ended on Monday. It was down 0.4% on Tuesday.

South Africa's rand stabilised after struggling power utility Eskom said it would shorten power cuts from Tuesday morning.

The currency lost 1.3% on Monday on worries about power outages, which are seen continuing at least into 2024, weighing on economic growth in the country.

There were also policy worries as the power shortages are a major source of frustration for voters ahead of 2024 elections that could see the governing African National Congress lose its majority in parliament for the first time.

Meanwhile, Ghana extended its domestic debt restructuring deadline until the end of January after the crisis-hit nation launched a debt-swap plan at the start of December. For GRAPHIC on emerging market FX performance in 2023, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2023, see https://tmsnrt.rs/2OusNdX

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(Reporting by Susan Mathew in Bengaluru; Editing by Sharon Singleton)