New York's main contract, West Texas Intermediate (WTI) for January delivery, gained 63 cents from Tuesday to close at $87.38 a barrel.
In London trade, Brent North Sea crude for January advanced $1.03 to $110.86 a barrel.
The WTI rally in New York had "quite a bit to do with the inventories dropping -- that was quite unexpected," said Bart Melek at TD Securities.
The US Department of Energy announced that the nation's crude supplies sank 1.5 million barrels in the week ended November 16, instead of the gain of 800,000 barrels expected by analysts polled by Dow Jones Newswires.
Gasoline stockpiles also unexpectedly fell, by 1.5 million barrels, while distillates, which include heating fuel, a closely watched fuel as winter approaches, dropped by 2.7 million barrels, four times more than estimated.
The declines suggested stronger demand in the world's biggest oil-consumer country, spurring prices higher.
Prices, which have been impacted over the past week by clashes between Israel and the Palestinians in the Gaza Strip, reacted little to the announcement by Egypt and the United States that hostilities would cease at 1900 GMT.
SEB analyst Filip Petersson expressed doubts over whether the cease-fire would hold -- and predicted market volatility in the coming days.
"I would be very positively surprised if it holds, but my expectation is that we could see several rounds of failed attempts or short cease-fires that add volatility to the oil market," he told AFP.
Trade was muted ahead of US market closures on Thursday in observance of the Thanksgiving holiday.
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