All rational one-loop Einstein-Yang-Mills amplitudes at four points

All four-point mixed gluon-graviton amplitudes in pure Einstein-Yang-Mills theory with at most one state of negative helicity are computed at one-loop order and maximal powers of the gauge coupling using D-dimensional generalized unitarity. The resulting purely rational expressions take very compact forms. We comment on the color-kinematics duality picture and a relation to collinear limits of pure gluon amplitudes.