High fuel prices and profit margins in refining crude oil boosted the fortunes of Royal Dutch Shell in the quarter from April to June.
Profits at fuel stations helped Shell beat its European rival BP
Shell increased earnings - measured by current cost of supply - by more than 20% in those three months to $7.6bn (£3.7bn), up from $6.3bn.
Meanwhile, profit at ExxonMobil for the same period was almost flat, dipping slightly to $10.26bn from $10.36bn.
Earlier this week, UK rival BP reported a fall in its second-quarter earnings.
It said that falling production and problems at its refineries were to blame.
ExxonMobil remains the world's biggest oil company, and reported the highest-ever annual profit by a US business in 2006.
But analysts said efficient management and the higher oil price helped Shell offset an anticipated 2% fall in production to steal a march on its UK and international rivals.
Analyst Keith Bowman of Hargreaves Lansdown Stockbrokers said that Shell's management creditability - which was damaged in 2004 after it had to cut estimates of its proven oil reserves by 20% - was continuing to recover.
"The group is not only further distancing itself from the woes which beset it just a few years ago but scores a victory over industry rivals as quarterly profits progress," he said.
"While both Shell and BP are suffering disappointing falls in production, management execution of operational issues at Shell appears to be the current defining difference between the two."
Shell's chief executive, Jeroen van der Veer, said the firm had delivered "another competitive set of results".
"Major projects are going well and our disposal programme adds more focus in the company," he said.
Production of oil and gas dropped 2% to 3.2 million barrels of oil equivalent per day, which was in line with analysts' expectations, Shell said.
While total crude oil production rose by 1%, Shell said that gas production had fallen 6%.
This was due to the impact of continuing security problems in Nigeria and reduced demand in north-west Europe, the firm said.
Earlier this year, Shell sold its majority stake in the Sakhalin-2 oil and gas project off Russia's Pacific coast to Gazprom.
The move came after Russian authorities repeatedly refused to grant it the necessary environmental certificates.
Shell has been in long-running talks with Iran about building the country's first liquefied natural gas (LNG) project.
However, Mr van der Veer said that it was growing costs and negotiations on the terms of the deal - rather than the threat of sanctions against Iran - which had delayed an agreement.