We report on a study of electric resistivity and magnetic susceptibility measurements in electron irradiated SrTi0.987Nb0.013O3 single crystals. Point-like defects, induced by electron irradiation, lead to an almost threefold enhancement of the residual resistivity, but barely affect the superconducting critical temperature (Tc). The pertinence of Anderson's theorem provides strong evidence for a s-wave superconducting order parameter. Stronger scattering leads to a reduction of the effective coherence length (ξ) and lifts the upper critical field (Hc2), with a characteristic length scale five times larger than electronic mean-free-path. Combined with thermal conductivity data pointing to multiple nodeless gaps, the current results identify optimally doped SrTi1−xNbxO3 as a multi-band s-wave superconductor with unusually long-range electrodynamics.