We present an application of the extended stochastic Liouville equation [G. M. G. McCaul, Phys. Rev. B 95, 125124 (2017)2469-995010.1103/PhysRevB.95.125124], which gives an exact solution for the reduced density matrix of an open system surrounded by a harmonic heat bath. This method considers the extended system (the open system and the bath) being thermally equilibrated prior to the action of a time-dependent perturbation, as opposed to the usual assumption that the system and the bath are initially partitioned. Our method presents an exact technique capable of accounting for arbitrary parameter regimes of the model. Here, we present our first numerical implementation of the method in the simplest case of a Caldeira-Leggett representation of the bath Hamiltonian, and apply it to a spin-boson system driven from coupled equilibrium. We observe significant behaviors in both the transient dynamics and asymptotic states of the reduced density matrix not present in the usual approximation.