We study targeted energy transfer (TET) in a coupled oscillator, consisting of a single‐degree‐of‐freedom primary linear oscillator coupled to a vibro‐impact nonlinear energy sink (VI NES). For this purpose, we first compute the VI periodic orbits of the underlying hamiltonian VI system, and construct the corresponding frequency‐energy plot (FEP). Then, considering inelastic impacts and viscous dissipation, we examine VI damped transitions on the FEP to identify a TET phenomenon by exciting a VI impulsive orbit, which is the most efficient mechanism for TET. Not only can the VI TET involve passive absorption and local dissipation of significant portions of the energy from the primary systems, but it occurs at sufficiently fast time scales. This renders VI NESs suitable for applications, like seismic mitigation, where shock elimination in the early, highly energetic regime of the motion is a critical requirement.