The foreign secretary teamed up again with Hollywood actress and UN envoy Angelina Jolie – with whom he has visited warzone rape victims – to push for the agreement, in speeches to the global body in New York.
G8 nations agreed in London in April to address the issue, and the UK is leading efforts to draw up international investigation and documentation standards to aid prosecutions.
If fully implemented, the measures in the resolution “will represent vital new advances in how we tackle rape and sexual violence in conflict,” Mr Hague said.
Ms Jolie said it was the clear responsibility of the United Nations to protect victims, but the “sad, upsetting and indeed shameful reality” was that hundreds of thousands of such crimes went unpunished because the issue was not given sufficient priority.
She said: “All countries have a responsibility to step forward. But the starting point must be you, the UN Security Council, shouldering your responsibilities and showing leadership.”