In this work we consider a system of partial differential equations of parabolic type under Markovian structural perturbations. Sufficient conditions for the stability and the convergence of the solution process of the system are given by developing a block comparison theorems in the context of Lyapunov-like functions. Moreover, an effort has been made to characterize the effects of random structural perturbations. In fact, it has been shown that the random structural perturbations are indeed the stabilizing agents. In addition, examples are given to illustrate the significance of the presented results