Dark matter annihilation in Galactic substructure will produce diffuse gamma-ray emission of remarkably constant intensity across the sky, making it difficult to disentangle this Galactic dark matter signal from the extragalactic gamma-ray background. We show that if Galactic dark matter contributes a modest fraction of the measured emission in an energy range accessible to the Fermi Gamma-ray Space Telescope, the energy dependence of the angular power spectrum of the total measured emission could be used to confidently identify gamma rays from Galactic dark matter substructure.