Analysts last week predicted strong surges in profit for BP, due to a rise in oil prices to $75 a barrel. This tops their initial prediction of $2.2 billion according to to a company-provided analytics survey.
Adjusted net income for the first quarter was $2.59 billion, the highest since 2014 and beating analysts' estimates of $2.12 billion.
First-quarter production rose to 3.7 million barrels per day, up 6% from a year earlier.
Bob Dudley added: "Moving through 2018 we're determined to keep delivering our operational targets and maintaining capital discipline while growing cash flow and returns".
Underlying profits were also up, with BP posting an underlying recurring cost profit of almost $2.6 billion, up from $1.5 billion a year earlier.
Over the longer term, our new lower carbon ambitions, including clear targets for our own emissions, will help ensure that all of BP is also focused on advancing the energy transition..More news: Deer found struck with arrows, troopers searching for suspect
"The spill payment in the first quarter was "$500 million more than I expected", although that probably means the burden will be lower later this year, said Redburn analyst Rob West, as quoted by Bloomberg.
"Underlying profit was up 23% on the previous quarter and was our best quarterly result in three years". Upstream production, excluding Rosneft, was 9% higher, supported by continued ramp up of major projects. That's the highest total production since the fourth quarter of 2010.
Despite the start-up of Atoll, BP warned on Tuesday that it expected output during the current quarter to be lower reflecting the expiration of the Abu Dhabi offshore concession and seasonal turnaround and maintenance activities. Natural gas averaged $3.50 per thousand cubic feet in the year-ago quarter, compared to $3.78 in the first quarter of this year.
Gulf of Mexico oil spill payments in the quarter were $1.6 billion on a pre-tax basis, including $1.2 billion for the final payment relating to the 2012 Department of Justice settlement. Payments are expected to be just over $3 billion in 2018, weighted to the first half of the year.
BP's ADSs closed up about 0.8% on Monday at $44.59, in a 52-week range of $33.90 to $44.89.
Investors are looking closely at cash flow as an indication of Big Oil's ability to pass on the rewards of higher prices through share buybacks.