Saturn is a source of intense kilometre-wavelength radio emissions that are believed to be associated with its polar aurorae, and which provide an important remote diagnostic of its magnetospheric activity. Previous observations implied that the radio emission originated in the polar regions, and indicated a strong correlation with solar wind dynamic pressure. The radio source also appeared to be fixed near local noon and at the latitude of the ultraviolet aurora. There have, however, been no observations relating the radio emissions to detailed auroral structures. Here we report measurements of the radio emissions, which, along with high-resolution images of Saturn's ultraviolet auroral emissions, suggest that although there are differences in the global morphology of the aurorae, Saturn's radio emissions exhibit an Earth-like correspondence between bright auroral features and the radio emissions. This demonstrates the universality of the mechanism that results in emissions near the electron cyclotron frequency narrowly beamed at large angles to the magnetic field.