The numerical analysis of closures and stabilizations for reduced-order models (ROMs) of convection-dominated buoyancy-driven flows is relatively scarce. In this paper, we take a step in this direction and conduct a numerical analysis of the evolve-filter-relax ROM (EFR-ROM), which uses spatial filtering to stabilize ROMs for convection-dominated flows. We establish stability and derive an a priori error bound for the EFR-ROM. Demonstrated in both 2D unsteady convection and 2D Rayleigh–Bénard convection test problems, our numerical investigation shows that the theoretical convergence rates are recovered numerically, and that the EFR-ROM yields more accurate velocity and temperature solutions, as well as the kinetic energy and Nusselt number, compared to the standard Galerkin ROM (G-ROM).