The survey by NatCen, a respected social research organisation, found that 93 per cent of Scots favored maintaining free trade with the EU, compared with 88 per cent in Britain as a whole.
On immigration, 64 per cent of Scots said EU and non-EU immigrants should be subject to the same controls, versus 68 per cent across Britain.
Scottish lawmakers to hold independence vote on eve of Brexit
The gap was wider on willingness to trade off between those two issues. In Scotland, 61 per cent said Britain should allow free movement of people in return for free trade with the EU, while the figure for the whole of Britain was 54 per cent.
Scots, who represent about 8 per cent of the UK population, voted to remain in the EU in last year's referendum while the United Kingdom as a whole voted to leave.
Political scientist John Curtice, author of the NatCen survey, said it did not support the view that Scots' greater support for EU membership would translate into a desire to break away from the UK to pursue their own relationship with Europe.
"It is far from clear that concerns about Brexit are likely to change the minds of many voters about the merits or otherwise of independence," he said. "So long, of course, as the UK government succeeds in delivering both free trade and immigration control."
Scottish parliament backs bid for new independence referendum
Scotland's devolved government, which is run by the pro-independence Scottish National Party (SNP), has said Scots should not be dragged out of the EU against their will.
It has called for a new referendum on independence in late 2018 or early 2019, arguing that Brexit meant circumstances had changed since Scots rejected independence in a 2014 vote.
The British government, which would have to give its consent for a second referendum, opposes Sturgeon's plan.
The Scottish government said the NatCen survey reflected Scots' enduring belief in the value of EU membership.
"The poll demonstrates people in Scotland continue to value the protections and rights offered by the EU, particularly on key issues such as free trade and freedom of movement," a Scottish government spokesperson said.
NatCen surveyed 859 people in Scotland and 2,322 people across Britain, online and by telephone, between Feb 5 and March 2.
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