We demonstrate how a time-dependent dissipative environment may be used as a tool for controlling the quantum state of a two-level atom. In our model system the frequency and coupling strength associated with microscopic reservoir modes are modulated, while the principal features of the reservoir structure remain fixed in time. Physically, this may be achieved by containing a static atom-cavity system inside an oscillating external bath. We show that it is possible to dynamically decouple the atom from its environment, despite the fact that the two remain resonant at all times. This can lead to Markovian dynamics, even for a strong atom-bath coupling, as the atomic decay becomes inhibited into all but a few channels; the reservoir occupation spectrum consequently acquires a sideband structure, with peaks separated by the frequency of the environmental modulation. The reduction in the rate of spontaneous emission using this approach can be significantly greater than could be achieved with an oscillatory atom-bath detuning using the same parameters.