The company's adjusted net profit, which excludes exceptional items, plunged by 86 percent from a year ago to $122 million (108 million euros) in the first quarter. The market consensus was for a slight loss.
In late trading, the Statoil share price was up 5.9 percent on the Oslo exchange, boosting the overall index which was up by 1.9 percent.
Statoil has implemented an aggressive savings programme, laying off staff and renegotiating supplier contracts.
"Operating costs and capex (capital expenditure) are falling faster than expected," said Pareto analyst Trond Omdal in a note quoted by Bloomberg news agency.
Statoil, 67-percent owned by the state, joins other oil groups BP of Britain and Total of France in surprising markets with stronger-than-expected earnings despite the low oil price.
"Our financial results were affected by low oil and gas prices in the quarter," Statoil chief executive Eldar Saetre said in a statement.
"We delivered strong operational performance across all business areas, high production efficiency and results in line with expectations from liquids trading and refining," he said.
Oil and gas production remained largely unchanged from a year ago, at 2.05 million barrels of oil equivalent per day, while the price for liquids fell 39 percent.
As the oil price gently rebounds, hovering around $47 on Wednesday in London, Saetre told financial daily Dagens Naeringsliv that Statoil aimed to keep its business profitable even with an oil price under $40.
Statoil's main businesses -- offshore, non-conventional oil and gas in North America -- have relatively high operating costs.
The company maintained its investment forecast for this year at $13 billion, and proposed a dividend of $0.22 per share in cash or new shares at a five-percent rebate.