The oil giant’s underlying replacement cost profit for the quarter came in at 1.819 billion US dollars (£1.185bn), compared with 3.037 billion US dollars (£1.979m) a year ago.
BP said the drop was a result of sharply lower oil and gas prices, which have more than halved to 50 dollars a barrel - compared with around 100 dollars 12 months ago.
However, the performance still comfortably exceeded analysts’ estimates of 1.2 billion US dollars (£780m) profit.
BP chief executive Bob Dudley said: “Last year, we acted decisively to reset BP for a sustained period of lower oil prices and the results are coming through well. We are now in action to rebalance our financial framework in this new price environment.
“And I am confident that BP’s strong and well-balanced portfolio of businesses and projects gives us the ability to grow value into the future.
“All of this underpins our strong priority of sustaining our dividend and then growing free cash flow and shareholder distributions over the long term.”
The firm also revealed that its total bill for the Deepwater Horizon oil spill has now hit 55 billion dollars (£35.85bn), and warned costs could yet rise further.
“The total amounts that will ultimately be paid by BP in relation to the incident will be dependent on many factors,” it said.
“These could have a material impact on our consolidated financial position, results and cash flows.”
Looking to the fourth quarter, BP said it expected production to be slightly higher than the third quarter thanks to planned seasonal turnaround activity.
The oil giant announced a quarterly dividend of 10 cents per ordinary share, which is expected to be paid on December 18. The corresponding amount in sterling will be announced on December 7, it added.