High-energy positron annihilation is a viable mechanism to produce dark photons (${A}^{\ensuremath{'}}$). This reaction plays a significant role in beam-dump experiments using multi-GeV electron beams on thick targets by enhancing the sensitivity to ${A}^{\ensuremath{'}}$ production. The positrons produced by the electromagnetic shower can produce an ${A}^{\ensuremath{'}}$ via nonresonant (${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}+{A}^{\ensuremath{'}}$) and resonant (${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{A}^{\ensuremath{'}}$) annihilation on atomic electrons. For visible decays, the contribution of resonant annihilation results in a larger sensitivity with respect to limits derived by the commonly used ${A}^{\ensuremath{'}}$-strahlung in certain kinematic regions. When included in the evaluation of the E137 beam-dump experiment reach, positron annihilation pushes the current limit on $ϵ$ downwards by a factor of 2 in the range $33\text{ }\text{ }\mathrm{MeV}/{c}^{2}<{m}_{{A}^{\ensuremath{'}}}<120\text{ }\text{ }\mathrm{MeV}/{c}^{2}$.