<p>Nonreciprocal physics is garnering enormous attention in both classical and quantum resource fields. Surprisingly, previous demonstrations have not explored nonreciprocal quantum synchronization of phonons, one of the most obvious examples of nonreciprocal quantum resources. Here we fill this gap to demonstrate the possibility of nonreciprocal quantum synchronization, revealing its counterintuitive robustness against random fabrication imperfections and thermal noise of practical devices. Specifically, phonons are synchronized in a chosen direction of light (magnetic field) but unsynchronized in the other, yielding a unique nonreciprocity of quantum synchronization. This happens by harnessing the synergy of the Sagnac and magnon-Kerr effects, leading to an opposite Sagnac-Fizeau shift and an exceptional magnon-Kerr-induced transition. Unlike previous proposals naturally restricted to the low-imperfection regime, our approach beats this limitation, owing to the magnon-Kerr-induced improvement in the resonator resilience. The study lays the foundation for generating fragile-to-robust nonreciprocal quantum resources.</p>