Nadia Murad was 21 years old when, she says, Islamic State fighters abducted her, beat her and raped her. Her offense: belonging to the minority Yazidi community, whom the Islamic State regards as infidels. Her cause for the last two years: demanding justice for the Islamic State’s atrocities.

This week, Ms. Murad clinched a small, but important victory. Her country, Iraq, agreed to let the Security Council appoint a panel of independent investigators to gather evidence of the most serious crimes committed by the Islamic State, and not just those against Yazidis. Lacking that, the Security Council would have had to adopt a resolution to create such a panel.

Still to be resolved is where and how those crimes will be prosecuted, and how to make sure those trials are credible and not displays of victor’s justice.

Ms. Murad’s quest poses an acute test for the promise of international justice, born from the ashes of Nazi genocide 70 years ago, after World War II.