Apart from resolved gamma-ray emitters, the extragalactic gamma-ray background (EGB) comprises emission from potentially undetected sources and may therefore serve as a valuable tool for their detection. While the classical approach of EGB decomposition manifests in combined spectral fits of individual contributions, statistical methods have been proven to be even more sensitive. In this contribution, we summarize recent attempts of using 1-point photon counts statistics for decomposing the EGB detected with Fermi-LAT, focusing on point-source contributions and the diffuse isotropic background contribution. For the first time, we generalize the analysis to incorporate a potential contribution from annihilating dark matter. This allows the derivation of new competitive upper limits on the dark matter self-annihilation cross section, which are complementary to upper limits obtained with other indirect detection methods.