An inner-shell vacancy in an atom can decay very efficiently via the emission of an Auger electron. Thus far, Auger decay has been observed in atoms, molecules and clusters following the ionization or excitation by light with high photon energies in the extreme-ultraviolet and X-ray regime. Surprisingly, we have discovered Auger decay after the interaction of methane clusters with intense near-infrared laser pulses, even though the photon energy is not sufficient to directly generate an inner-shell vacancy. However, due to very efficient ionization avalanching in clusters, electrons from outer as well as inner shells are removed from their atoms during the laser pulse, and a nanoscale plasma is formed. Subsequent recombination of electrons to outer shells of ions and to high-lying Rydberg orbitals then results in a population inversion of the cluster atoms. By observing a clear peak in the electron spectrum, evidence was provided for the first time that Auger decay is one of the relaxation channels of the highly excited system. In the future, the observed population inversion could be exploited for the development of a table-top X-ray laser.