The Mpemba effect is the counterintuitive phenomenon, where some states relax faster than others despite being initially farther from equilibrium. In quantum systems, realizing this effect typically requires fine-tuned dissipation or carefully engineered initial states, making it fragile to disorder. Here, we uncover a robust statistical quantum Mpemba effect arising from Griffiths rare-region physics in a one-dimensional dissipative lattice. Sparse local losses fragment the system into random loss-free regions that host long-lived quasi-bound modes with broadly distributed lifetimes. We show that simple extended Bloch states, although having identical density profiles, couple very differently to these modes: a uniform state predominantly excites slowly decaying modes, while a phase-modulated state couples more strongly to rapidly decaying ones. This mismatch produces a disorder-robust inversion of relaxation times, where the initially “farther” state relaxes faster. Our results identify Griffiths rare-region physics as a robust mechanism for quantum Mpemba dynamics in disordered quadratic open quantum systems.