High-energy positron annihilation is a viable mechanism to produce dark photons (A′). This reaction plays a significant role in beam-dump experiments using multi-GeV electron beams on thick targets by enhancing the sensitivity to A′ production. The positrons produced by the electromagnetic shower can produce an A′ via nonresonant (e++e−→γ+A′) and resonant (e++e−→A′) 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′-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  MeV/c2<mA′<120  MeV/c2.