By Sarah Kent, Justin Scheck and Inti Landauro 

LONDON-- BP PLC of the U.K. and Total SA of France each reported sharply lower quarterly profits on Tuesday while providing glimpses into how the world's largest oil companies are weathering the depths of an oil-price crash.

BP's version of net income plunged by 40% from a year earlier and its cash flow nose-dived more than 75%, while Total's net profit fell by 20%. Both companies saw their revenues from oil sales plummet as crude traded for about $54 a barrel in the first quarter of 2015, half its price a year earlier.

In a sign of how bad things have been for big oil companies, those numbers were seen as being better than expected. Three months ago, Total reported a $5.7 billion loss for the fourth quarter of 2014, while BP's losses totaled almost $1 billion.

This time around, BP and Total--the world's fourth- and fifth-largest independent oil companies by market value--were helped by increased production, deep cost cuts and healthy profits from their refining businesses. To some industry observers, the results indicate that oil companies may be able to cope with low prices better than many investors expected.

"The dire earnings collapse is not going to be as bad as generally anticipated," said Brian Youngberg, an analyst at Edward Jones.

Two other huge oil companies, Exxon Mobil Corp. and Royal Dutch Shell PLC, will reveal on Thursday whether similar measures worked for them during the downturn. Italian energy giant Eni SpA reports results on Wednesday, while Chevron Corp. comes out on Friday.

BP and Total demonstrated the advantages of an integrated oil company--one that explores for oil, extracts it, refines it and sells it to customers--when oil prices drop. Easing the damage were their downstream operations, which refine, ship and trade oil and gas. BP's profits from its downstream operations more than doubled year on year, while Total saw its operating income from its refining and petrochemicals division almost tripled.

Total is "profiting from its integrated model," Chief Executive Officer Patrick Pouyanné said.

For BP, the results come at an uncertain moment. It has been trying to simultaneously weather the oil slump and come back from its massive spill in the Gulf of Mexico five years ago. Its shrinking size made it the subject of takeover talk in the wake of rival Royal Dutch Shell PLC's $70 billion deal to buy BG Group PLC (though a U.K. official says the government would move to block a foreign acquisition of BP).

BP was aided in the latest quarter by a U.K. tax break for companies operating in the North Sea, though it didn't quantify the benefit. Mr. Gilvary said the company is continuing with a program of cost cuts, slashing staff, cutting capital spending and trying to reduce other expenses. First-quarter capital expenditures fell by almost 20% from a year earlier to $4.4 billion. Mr. Gilvary said the company has sold more than $7 billion in assets as part of a $10 billion planned selloff to end this year. The company has already committed to cut capital spending by 20% this year to $20 billion.

BP and Total both said their trading arms had capitalized on the market's condition after the slump in oil prices created a contango, in which current oil prices are cheaper than those in the future. That lets traders store oil they bought at low prices while locking in a profit by selling pricier futures.

As BP unwinds its position throughout the year, more cash could return to its balance sheet. While BP rarely provides details on its trading performance, Chief Financial Officer Brian Gilvary said trading results last quarter were $300 million to $400 million better than normal.

Ivor Pether, a fund manager at Royal London Asset Management, said the quarterly results offer some encouragement that BP can deliver on its cost-cutting plans. Royal London held more than $680 million in BP stock as of earlier this month.

But, he added, "I'm terribly wary of interpreting too much from the quarterly figures," since some savings and trading profits are "not necessarily repeatable."

Total was helped by the fact that many of its aggressive investment projects, carried out when oil prices were much higher, are due to start pumping oil and gas.

During the first quarter of this year, Total increased production by 10% to 2.4 million barrels of oil equivalent a day, the strongest increase in a decade. The company attributed this to the start of several projects in the North Sea and in Nigeria, an increase of production in Angola and the recent partnership signed with Abu Dhabi.

The bottom line in the first quarter was also lifted by capital gains worth about $1 billion from the sale of such assets as its petrochemical unit Bostik and minority stakes in oil fields in Nigeria.

But there were also warning signs. Total wrote down $659 million on the value of its assets in Libya given the impact of the violence in the country, and $93 million on its assets in Yemen as political instability has recently worsened.

Moreover, the company said the improved performance of its refining business only marked a brief respite in an industry that has long suffered from overcapacity. Refining margins have already started to fall, Total said.

"Using the first quarter as a proxy for the full year would not be correct," Total's Chief Financial Officer Patrick de la Chevardière said in a conference call with analysts.

Write to Sarah Kent at sarah.kent@wsj.com, Justin Scheck at justin.scheck@wsj.com and Inti Landauro at inti.landauro@wsj.com

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