The Fano effect arising from the interference between two dissipation channels of the radiation continuum enables tuning of the photon statistics. Understanding the role of the Fano effect and exploiting it to achieve strong photon correlations are of both fundamental and applied significance. We present an analytical description of Fano-enhanced photon correlations based on cavity quantum electrodynamics to show that the Fano effect in atom-cavity systems can improve the degree of antibunching by over four orders of magnitude. The enhancement factors and the optimal conditions are explicitly given, and found to relate to the Fano parameter q. Remarkably, the Fano enhancement manifests robustness against the decoherence processes and can survive in the weak coupling regime. We expect our work to provide insight to tuning the photon statistics through the Fano effect, which offers a new, to the best of our knowledge, route to enhance the photon correlations, as well as the possibility of generating nonclassical light in a wider diversity of systems without the need of a strong light-matter interaction.