The group posted underlying replacement cost profits - the benchmark industry measure - of 933 million US dollars (£762.8 million) for the three months to the end of September against 1.82 billion US dollars (£1.49 billion) a year earlier.
BP warned oil refining margins would continue to take a hit in the final three months of the year, but it added it expects production to increase slightly in the fourth quarter.
The group is slashing costs in the face of weak oil global oil prices and sliding refining margins, with the cost of crude at around 46 US dollars a barrel in the third quarter compared with 50 dollars a year ago.
Brian Gilvary, BP’s chief financial officer, said: “We continue to make good progress in adapting to the challenging price and margin environment.”
On a statutory basis, replacement cost profits rose 35% to 1.66 billion US dollars (£1.36 billion) as it ramped up cost-cutting.
BP said it now sees annual costs coming in even lower than previously expected, at around 16 billion US dollars (£13.1 billion), down from the range of 17-19 billion US dollars (£14-16 billion) originally pencilled in.
Underlying earnings for the first nine months of the year more than halved to 2.2 billion US dollars (£1.8 billion) as its bill for the Deepwater Horizon oil spill surged to 61.8 billion US dollars (£50.4 billion).
It said on reporting second-quarter results earlier this year that it hoped to draw a line under the payouts for the Gulf of Mexico disaster in 2010, with settlements now coming to a close.