To simulate spatially inhomogeneous bimolecular reactions driven by diffusion and tunneling we suggest a new stochastic algorithm which combines the well known Random Walk on Spheres (RWS) method and the kinetic Monte Carlo algorithm. This drastically decreases the computer time in the case of diffusion, and especially for low concentrations. This is the case, for instance, when the annihilation of spatially separate electrons and holes in a disordered semiconductor is studied. The method treats all kinds of reactions involved in a unified stochastic kinetic scheme. In particular, along the diffusion and tunneling, nonradiative recombinations in defect sites are taken into account. To validate the simulation algorithm, we compare our simulation results with the asymptotics of the intensity of annihilation which is known from theoretical predictions. Also, we compare the stochastic algorithms with finite-difference methods.