BP's downstream operations - its refining and petrol sales business - made an underlying pre-tax profit of $1.3bn, up 70% from the same period last year.
Despite benefitting from the high price of oil, BP said it had also benefited from "very real operational improvements in refining and rigorous cost control across the company".
BP also saw overall production levels rise slightly from a year earlier, despite commentators predicting a minor fall.
Analyst Tony Shepard of Charles Stanley said BP's results were "way above the market expectations".
Richard Hunter, head of UK equities at Hargreaves Lansdown Stockbrokers, was equally impressed.
"These numbers have comfortably surpassed the top end of expectations and reiterate BP's position as a true oil major."
Russian problems
BP's Russian joint venture TNK-BP has been dogged by a power struggle this year.
The dispute between BP and the group of Russian billionaires that control the other 50% of the business led to the departure of former TNK-BP chief executive Robert Dudley last month.
Mr Dudley said he had faced "sustained harassment".
The Russians, who owned their stake in TNK-BP through a consortium known as Alfa Access Renova, had accused Mr Dudley of favouring BP.
Mr Dudley's departure came as BP signed an agreement aimed at ending the dispute that will include the appointment of three independent directors.
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