In this paper, we analyze the dynamics of complex balanced single-substrate single-product (SS) chemical reaction networks governed by mass-action kinetics with a carefully chosen set of boundary species fixed at constant concentrations. The remaining species of the reaction networks are allowed to have constant influx and/or proportional efflux. We show that such a network has a unique equilibrium concentration vector in the positive orthant and it is asymptotically stable. Using the maximum modulus principle for graphs, we provide bounds for this equilibrium.