The proportion of children in poverty dropped 10 percentage points in the decade to 2011/12, compared with six percentage points in England, according to a report by the New Policy Institute (NPI) for the Joseph Rowntree Foundation (JRF).
Despite this success, the charity warned progress had stalled as it published the first of three referendum briefings ahead of the vote on September 18.
More than half (54%) of children in workless families in Scotland are in poverty, compared with 10% of those in working families.
Changes to benefits are likely to have increased poverty for children in workless families further, the report says.
Tackling the issue must be a priority for governments at Holyrood and Westminster regardless of the referendum outcome, JRF Scotland advisor Jim McCormick said.
"Progress on reducing child poverty has stalled after a steady reduction and the rate is set to rise again," he said.
"The challenge for each side of the referendum campaign is to demonstrate how a country where no child grows up and remains in poverty can be achieved."
The overall level of child poverty in Scotland was 17% before housing costs in 2011/12, the analysis shows.
Much of the improvement in both England and Scotland is due to a drop in the poverty rate among lone-parent families, the report said.
Scotland's better record is attributed to an additional reduction in poverty among working couples who have children.
There appears to have been a shift in this group north of the border towards both adults being in work, which the authors said had not happened in England.
Dr Peter Kenway, director of the NPI and report co-author, said: "This is probably due to parents in Scotland being better able to access suitable jobs with adequate pay and services such as childcare and transport.
"But how much credit policy makers, in either Edinburgh or in London, can take for this is unclear."
Poverty in families with no-one in work remains high and must be tackled if the rate is to be brought down further, the report said.
It states: "In the midst of significant welfare reforms by the UK Government, the Scottish Government can only play a limited role but it has absorbed the cut to Council Tax Benefit, replaced the abolished components of the social fund and provided compensation to some families affected by the the under-occupancy charge, or 'bedroom tax'.
"This could prevent Scotland's workless poverty rates from worsening as quickly as it would otherwise."
Dr Kenway added: "Scotland's challenge is to find a route out of poverty for the many families that are out of work.
"This means people with ill-health and disabilities, caring duties and those with a lack of skills. People in such households must be offered a sustainable route out of poverty as well as continuing to reduce in-work poverty."
JRF will publish two more briefings on housing and work in Scotland before the referendum.
John Dickie, head of the Child Poverty Action Group in Scotland, said: "After a decade or more of very real progress independent forecasts now suggest an explosion in child poverty as a result of current UK government tax and benefit policy.
"This JRF briefing highlights the need to focus support on families who are unable to work as well as those in work.
"The challenge now for all sides in the independence debate is to help build the public support and political will needed to invest in social security and childcare as well as create a far fairer distribution of rewards and opportunities in the workplace, wherever powers end up lying."