Intramolecular vibrational energy redistribution (IVR) plays a significant role in cavity-modified chemical reaction rates. As such, understanding the fundamental mechanisms by which the cavity modifies the IVR pathways is a fundamental step toward engineering the effect of the confined electromagnetic modes on the outcome of chemical processes. Here we consider an ensemble of M two-mode molecules with intramolecular anharmonic couplings interacting with an infrared cavity mode and consider their quantum dynamics and infrared spectra. Polaritonic Fermi resonances involving fundamental and overtone states of the polaritonic subsystem mediate efficient energy transfer pathways between otherwise off-resonant molecular states. These pathways are of collective nature, yet enabled by the intramolecular anharmonic couplings. Hence, through polaritonic Fermi resonances, cavity excitation can efficiently spread toward low-frequency modes while becoming delocalized over several molecules.