The fundamental phenomenon of Bose-Einstein Condensation (BEC) has been observed in different systems of real and quasi-particles. The condensation of real particles is achieved through a major reduction in temperature while for quasi-particles a mechanism of external injection of bosons by irradiation is required. Here, we present a novel and universal approach to enable BEC of quasi-particles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. After heating to an elevated temperature, a sudden decrease in the temperature of the phonons, which is approximately instant on the time scales of the magnon system, results in a large excess of incoherent magnons. The consequent spectral redistribution of these magnons triggers the Bose-Einstein condensation.