* Fed cuts bond buying in first step away from historic stimulus
* Asia shares climb on Fed commitment, dollar jumps
* U.S. crude stocks at Cushing fall, EIA says, as pipeline starts fill
* South Sudan army says loses town as fighting spreads
SINGAPORE, Dec 19 (Reuters) - Brent futures slipped towards $109 a barrel on Thursday after shrugging off in the previous session the U.S. Federal Reserve's move to taper its monetary stimulus.
Chairman Ben Bernanke and his team embarked on the risky task of winding down the era of easy money, saying the U.S. economy was finally strong enough for the bank to start scaling down its massive bond-buying stimulus.
That boosted the U.S. dollar, a negative for oil as it made it pricier for holders of other currencies to buy. Oil, though, was supported by the unfolding crisis in South Sudan.
Brent crude slipped 24 cents to $109.39 a barrel by 0225 GMT, after settling $1.19 higher overnight. U.S. oil fell 14 cents to $97.66, after ending 58 cents up.
"Markets were worried that speculative money was going to come out. But what the Fed announced was an incremental change rather than a huge change," said Tony Nunan, oil risk manager at Mitsubishi Corp in Tokyo.
"The Fed had also said they would not taper till they were sure the economy could handle it. That, and supply worries are supporting prices," Nunan added.
The central bank's asset-purchase program, a centerpiece of its crisis-era policy, was to kick-start hiring and growth to help the economy recover from the recession. Its first program was launched during the 2008 financial crisis.
Brent prices are caught in a range between $107.39 and $110 a barrel, Nunan said. The European benchmark may break past the top end of the range because of lingering supply worries amid steady winter demand, he said. That will push the contract to a higher trading range, of $110 and $113.
The U.S. benchmark may also move to a higher range and trade between $96 and $102 a barrel if there is a sustained drawdown in crude stockpiles in the world's biggest oil consumer, from its current $95 to $99 range, he said.
SUDAN, US CRUDE STOCKS
Investors are watching the unfolding crisis in South Sudan, which has stoked supply disruption worries for a market already coping with losses from Libya.
South Sudan's army said it had lost control of the flashpoint town of Bor, its first acknowledged reversal in three days of clashes between rival groups of soldiers that have triggered warnings of a slide into civil war.
Further declines in oil were also limited by Energy Information Administration data that showed U.S. inventories of crude across the country fell 2.94 million barrels, more than the 2.3 million barrels expected by analysts polled by Reuters.
Crude stocks at Cushing, Oklahoma, fell 600,000 barrels in the week ended Dec. 13, the EIA said, as a pipeline from the oil storage hub to the Gulf Coast began filling prior to starting operations.
Gasoline stocks rose 1.34 million barrels to 220 million barrels, less than the 1.9 million barrels expected, while distillates fell 2.11 million barrels to 116 million barrels, against a forecast of a small build of 400,000 barrels.
(Editing by Muralikumar Anantharaman)