Common-envelope events (CEEs), during which two stars temporarily orbit within a shared envelope, are believed to be vital for the formation of a wide range of close binaries. For decades, the only evidence that CEEs actually occur has been indirect, based on the existence of systems that could not be otherwise explained. Here we propose a direct observational signature of CEEs arising from a physical model where emission from matter ejected in a CEE is controlled by a recombination front as the matter cools. The natural range of time scales and energies from this model, as well as the expected colors, light-curve shapes, ejection velocities, and event rate, match those of a recently recognized class of red transient outbursts.