The Ipsos MORI poll was based on the same sample used by newspapers earlier this week which put overall support for a Yes vote in favour of independence at 32%, compared to 55% who would vote No.
Reform Scotland asked an extra set of questions, which showed 29% for the status quo, 27% for independence, but 41% in favour of remaining "part of the UK with the increased powers outlined in the Devo Plus proposal".
It also asked who should be responsible for raising most of the money the Scottish Parliament spends, with 61% saying the Scottish Government and 29% the UK Government. Asked whether the pro-Union parties should campaign for more powers for Holyrood as the alternative to independence, 66% agreed, while only 17% disagreed.
Ben Thomson, chairman of the think-tank behind the Devolution Plus proposal, said: "This poll is further proof of what we have suspected for some time – the current debate on Scotland's constitutional future is not adequately serving the people of Scotland because it is largely ignoring their preferred way forward.
"In a poll on the preferred route forward, neither the status quo nor independence can muster even 30% support, while Devo Plus polls over 40%.
"Most Scots have identified the key problem with the current devolution settlement – that the Scottish Parliament is not properly accountable for raising the money it spends. With twice the number of people believing that the Scottish Government should raise most of this money rather than the Westminster Government, we would urge all political parties to consider whether they are adequately representing popular demand."
He added: "It's time for the parties to lay their cards on the table. It's time people know exactly what they're voting for, and if nobody is offering Devo Plus – the most popular option – the question must be: why not?"
Jeremy Purvis, leader of the Devo Plus Group, said: "This is the first substantive test of opinion in Scotland on the Devo Plus proposals and shows very clearly the desire of the Scottish people to improve on the status quo, but rejecting independence. The very clear support for Devo Plus as the best way forward for Scotland should be listened to.
"The evidence is also clear that the vast majority of people would like the parties that do not support independence to work together to progress the case for Devo Plus. Devo Plus is not a tactic to defeat independence, rather it is a carefully considered way forward for a stronger Scotland within the UK."
Labour MSP Patricia Ferguson said: "This poll really makes the case for devolution. But Scotland now urgently needs to make a decision on whether or not we are part of the UK. Devolution – of whatever flavour – is not a stepping-stone on the way to independence, so before we decide how best Scotland's place in the UK develops, we need to decide whether or not we are part of the UK."
A Scottish Government spokeswoman said: "The vital issue is that the terms and timing of the referendum, including whether there is a 'more powers' option, are matters to be decided in Scotland, not imposed by Westminster."