We present a Regge-plus-resonance (RPR) description of the p(e,eK^+)Y processes (Y=Lambda,Sigma^0) in the resonance region. The background contributions to the RPR amplitude are constrained by the high-energy p(gamma, K^+)Y data. As a result, the number of free model parameters in the resonance region is considerably reduced compared to typical effective-Lagrangian approaches. We compare a selection of RPR model variants, originally constructed to describe $KY$ photoproduction, with the world electroproduction database. The electromagnetic form factors of the intermediate N^*s and $Delta^*s are computed in the Bonn constituent-quark model. With this input, we find a reasonable description of the p(e,eK^+)Y data without adding or readjusting any parameters. It is demonstrated that the electroproduction response functions are extremely useful for fine-tuning both the background and resonant contributions to the reaction dynamics.