The Supreme Court unanimously ruled in favour of Rebecca Steinfeld, 37, and Charles Keidan, 41, from London.
The court said the Civil Partnership Act 2004 – which only applies to same-sex couples – is incompatible with the European Convention on Human Rights.
Ms Steinfeld said she hoped the government does the “right thing” and extends civil partnerships to all.
“We are feeling elated,” she told the BBC outside court. “But at the same time we are feeling frustrated the government has wasted taxpayers’ money in fighting what the judges’ have called a blatant inequality.”
The judgement does not oblige government to change the law, although it does make it more likely that the government will now act, the BBC’s legal correspondent Clive Coleman explained.
In a civil partnership, a couple is entitled to the same legal treatment in terms of inheritance, tax, pensions and next-of-kin arrangements as marriage.
The couple, who met in 2010 and have two children, said the “legacy of marriage” which “treated women as property for centuries” was not an option for them.
“We want to raise our children as equal partners and feel that a civil partnership – a modern, symmetrical institution – sets the best example for them,” they explained.