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We present a new method to characterize unresolved point sources (PSs) generalizing traditional template fits to account for non-Poissonian photon statistics. We apply this method to Fermi Large Area Telescope γ-ray data to characterize PS populations at high latitudes and in the Inner Galaxy. We find that PSs (resolved and unresolved) account for ∼50% of the total extragalactic γ-ray background in the energy range ∼1.9 to 11.9 GeV. Within 10° of the Galactic Center with |b|≥2°, we find that ∼5%-10% of the flux can be accounted for by a population of unresolved PSs distributed consistently with the observed ∼GeV γ-ray excess in this region. The excess is fully absorbed by such a population, in preference to dark-matter annihilation. The inferred source population is dominated by near-threshold sources, which may be detectable in future searches.