The finding suggests 64% would prefer to share the proceeds, compared with 30% who think the revenue should stay in Scotland.
The YouGov poll, compiled by Better Together, also suggests most Scots want to share pensions and benefits across the UK.
Labour released the findings ahead of the launch of its referendum campaign, due to take place at a rally in Glasgow on Tuesday.
Scottish leader Johann Lamont will be joined by former prime minister Gordon Brown at the event.
Ms Lamont said: "According to this Better Together polling, most Scots understand that our pensions and benefits are better being backed across the United Kingdom, spread across 60 million people rather than six million.
"On oil, it is clear that Scots see the value of sharing out the volatility and uncertainty of oil revenues across the UK rather than being reliant on it as part of a smaller economy. We Scots want to share the benefits of oil throughout the UK and the UK wants to share the wealth of London with us Scots.
Mr Brown said: "Scots have contributed to the UK all of their lives, they have made their national insurance payments and paid their UK taxes. They think that the UK should continue to honour their promises. They are right."
The poll suggests 79% of Scots think the old age pension should be the same across the UK.
It shows 70% want corporation tax to remain the same, rather than allow a different rate in Scotland as proposed by the SNP.
Some 69% of Scots think the cost of paying benefits to people in Scotland should come from taxes collected across the UK.
The poll of 1,051 Scottish adults was carried our between May 14 and 18.
The SNP pointed to other polling which appears to contradict the findings.
"From the bedroom tax to child benefit cuts, and the squandering of North Sea revenues, Westminster's stewardship of welfare and the economy has caused untold harm to communities across Scotland - which is why the most recent Scottish Social Attitudes survey shows that 63% of people in Scotland want decisions about welfare, pensions and oil revenues to be made in Scotland, not Westminster," an SNP spokesman said.
"The much more substantial Scottish Social Attitudes survey contradicts this Labour Party poll.
"Only a Yes vote gives us the powers we need to create a fairer welfare system and an economy that works for Scotland, rather than a Westminster system which penalises the poorest people in our society."