We prove that a relevant part of the Lyapunov spectrum and the corresponding Oseledets spaces of a quasi-compact linear cocycle are stable under a certain type of random perturbation. The basic approach is a graph-transform argument. The result applies to the spectrum of (not necessarily i.i.d.) randomly perturbed expanding maps and yields generalizations of results recently obtained by Baladi, Kondah and Schmitt [5] with different methods.