BEIJING (Reuters) - China's services sector grew marginally faster in November as new orders rose at their quickest pace in 2-1/2 years, a private survey showed, an encouraging sign of strength that contrasts sharply with the gloom in the other parts of the economy.

The HSBC/Markit Services Purchasing Managers' Index (PMI) inched up to 53.0 last month from October's 52.9, above the 50-point level that separates growth from contraction in activity on a monthly basis.

New orders were especially buoyant. The new business sub-index climbed to 54.2 in November from 53.1 the previous month, a high not seen since May 2012.

The resilience in the services sector compares with cooling growth in Chinese factories. A pair of manufacturing PMIs showed earlier this week that growth in factories in November slid to lows unseen in at least six months.

The dour factory reports were the latest in a run of underwhelming data from the world's second-largest economy, and reinforced bets that authorities could further loosen fiscal and monetary policy in coming months to stoke growth.

"Downside pressures on the economy still persist," said Qu Hongbin, an economist at HSBC in Hong Kong. Qu said he expected further policy easing in coming weeks.

After saying for months that China doesn't need any big economic stimulus, the central bank unexpectedly cut interest rates on Nov. 21 by 40 basis points, its biggest reduction since November 2008 at the height of the global financial crisis.

Hurt by a sagging housing market, slowing domestic demand and investment and unsteady export sales, China's economy is forecast by some analysts to be headed towards its worst slowdown in 24 years this year with annual growth at 7.4 percent.

In a sign that companies were feeling the drag of an unsteady economy, a sub-index for business expectations for the year ahead dipped to a three-month low even though it stayed well above the 50-point level.

But firms were still hiring, with an employment sub-index hovering above 50 as some companies expanded their businesses, HSBC/Markit said.

Input prices also rose as some companies reported spending more on labour as they increased staff numbers.

Firms that were doing well passed on such cost increases to their clients by raising prices, HSBC/Markit said.