We study a mechanism through which the cosmic dark matter density can be explained simultaneously with the observed baryon asymmetry of the Universe. At the core of our proposal lie the out-of-equilibrium scattering processes of bath particles which are responsible for the production of feebly-interacting dark matter. The same processes violate $CP$, which further leads to an asymmetry between matter and antimatter being generated in the visible sector. We focus on the possibility that these interactions are described through nonrenormalizable operators, which leads to both dark matter and the baryon asymmetry being produced at high temperatures. The mechanism is exemplified by studying two concrete scenarios, one involving scalar and one involving fermion dark matter. We find that in both cases it is, indeed, possible to achieve a common explanation for the dark matter content and the matter-antimatter asymmetry of the Universe, provided that dark matter is in the keV mass range.