Measurements of the differential production of electrons from open-heavy-flavor hadrons with charm- and bottom-quark content in p+p collisions at √s=200  GeV are presented. The measurements proceed through displaced-vertex analyses of electron tracks from the semileptonic decay of charm and bottom hadrons using the PHENIX silicon-vertex detector. The relative contribution of electrons from bottom decays to inclusive heavy-flavor-electron production is found to be consistent with fixed-order-plus-next-to-leading-log perturbative-QCD calculations within experimental and theoretical uncertainties. These new measurements in p+p collisions provide a precision baseline for comparable forthcoming measurements in A+A collisions.