We study the effect of disorder on the particle density evolution in a classical Hamiltonian drivenlattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence ofstrong tails in the density distribution which even increases towards larger positions is shown, thusyielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, weidentify the conversion between different components of the unperturbed systems mixed phasespace which is induced by the disorder. Based on the introduction of individual conversion ratesbetween chaotic and regular components, a theoretical model is developed which correctly predictsthe scaling of the particle density. The effect of disorder on the transport properties is studiedwhere a significant enhancement of the transport for cases of localized disorder is shown,thereby contrasting strongly the merely weak modification of the transport for global disorder.