<p>In this work, we reconsider the classical, non-linear set of ordinary differential equations for Michaelis-Menten kinetics of enzyme reactions. As the first contribution, we prove non-negativity, boundedness by two conservation properties, existence and uniqueness globally in time of solutions to this time-continuous model. As the second contribution, we show that the unique equilibrium state is globally asymptotically stable by application of LaSalle’s invariance principle through a suitable Lyapunov function. As the third and main contribution, we introduce a non-standard finite-difference-method based on the implicit Eulerian time-stepping method for the discretization of the time-continuous dynamical system. We reformulate its numerical solution algorithm by an explicit scheme and demonstrate that all desirable properties of the time-continuous model transfer to the proposed time-discrete variant. Finally, we highlight the theoretical findings by numerical experiments.</p>