Partial suppression of the spectral diffusion of quantum dot (QD) excitons tuned to resonance of a nano-photonic cavity is reported. The suppression is caused by the Purcell enhancement of the QD-exciton recombination rate, which alters the rate of charging of the solid-state environment by the QD itself. The effect can be used to spectrally-stabilize solid-state emitters of single photons and other non-classical states of light.