Markets tumbled last week after polls pointed to a win for the "Leave" camp in today's crucial referendum, but they have rallied over the past four days as the pro-EU campaign recovered momentum.
Some analysts warn that a British exit could see the country tumble into recession with global spillover effects.
US benchmark West Texas Intermediate for August delivery advanced 98 cents to USD 50.11 a barrel on the New York Mercantile Exchange.
In London, Brent North Sea crude for delivery in August, the global benchmark, jumped to USD 50.91 a barrel, gaining USD 1.03 from yesterday's settlement.
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The final results of the Brexit referendum are not expected until about 0800 GMT tomorrow.
"Despite polls showing a tightly contested result, the markets are firmly convinced that the pro-EU camp will win," Commerzbank analyst Carsten Fritsch said.
The oil market had weakened yesterday as well due to a smaller-than-expected fall in US crude inventories, adding to concerns about the strength of demand and abundant global supplies.
Adding to the bearish tone was an unexpected rise in gasoline inventories, by 600,000 barrels, as the US summer driving season gets into gear.