New York's main contract, light sweet crude for delivery in December, jumped $1.29 to $81.73 per barrel.
Brent North Sea crude for January added $1.34 to $84.62 a barrel in London trade.
"Oil prices rebounded ... as the US dollar slid against a stronger euro following news that Dublin agreed to work closely with European Union-IMF on urgent measures regarding its debt issues," said Sucden analyst Myrto Sokou.
"Consequently, concerns eased about eurozone's economic stability and helped the euro to move higher against the dollar, adding some support to crude oil prices."
The euro rallied to $1.3657, which compared with 1.3530 late in New York on Wednesday, as Ireland appeared set for a massive bailout from the European Union and the International Monetary Fund, dealers said.
A weaker greenback boosts dollar-priced crude oil, which becomes cheaper for buyers using stronger currencies.
The energy market was also bolstered by bargain-hunting, after heavy losses earlier this week, while traders also digested an unexpectedly sharp drop in US crude stockpiles.
The US government's Department of Energy (DoE) said Wednesday that American crude inventories tumbled by 7.3 million barrels in the week to November 12.
That was the biggest weekly drop for 15 months and much weaker than the 100,000-barrel decline expected by the market.
The news helped push prices upwards, said Victor Shum, senior principal of Purvin and Gertz energy consultants in Singapore.
"The inventory report, which shows declines in crude stocks and also product stocks, is generally supportive and therefore we have a reaction to the inventory report," he added.
Gasoline reserves sank by 2.7 million barrels, whereas analysts had predicted a smaller drop of 600,000 barrels.
Recent falls in crude prices were also enticing people to buy up crude, Shum said.
"Some people view it as a buying opportunity," he said.
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