We study the role of perturbative unitarity in the resonant annihilation of two dark matter particles into the standard model bath. Systematically including all kinematically allowed holomorphic cuts of the corresponding forward-scattering diagram, cancellation of the singularities occurs, resulting in a fixed-order correction to the narrow-width approximation for the annihilation cross section. Unlike the standard approach based on including the finite width of the mediator, no double-counting of intermediate states occurs.