Three judges at the Court of Appeal in London ruled in their favour following a hearing in November.
One case, brought by A - a single mother living in a three-bedroom council house fitted with a secure panic room to protect her from a violent ex-partner - concerns the effect of the policy on women living in Sanctuary Scheme homes.
The other, brought by grandparents Paul and Sue Rutherford, of Clunderwen, Pembrokeshire, involves its impact on seriously disabled children who need overnight care.
In both cases it was argued that the policy, which came into force in April 2013, unlawfully discriminates against women and domestic violence victims and against children in the situation of the Rutherfords' grandson, Warren.
The Government rejects the term ''bedroom tax'' and says the regulations remove what is in fact a ''spare room subsidy'', with the aim of encouraging people to move to smaller properties and save around £480 million a year from the housing benefit bill.
Lord Chief Justice Lord Thomas, Lord Justice Tomlinson and Lord Justice Vos announced that they were allowing the appeals in both cases on the ground that the "admitted discrimination in each case ... has not been justified by the Secretary of State".
The Department for Work and Pensions (DWP) was given permission to challenge the Court of Appeal's ruling at the Supreme Court.