The ultimate limits of performance for any classical optical system are set by sub-wavelength fluctuations within the host material, which may be frozen-in or even dynamically induced. The most common manifestation of such subwavelength disorder is Rayleigh light scattering, which is observed in nearly all waveguiding technologies today and can lead to both irreversible radiative losses as well as undesirable intermodal coupling, While it has been shown that backscattering from disorder can be suppressed by breaking the time-reversal symmetry in magneto-optic and topological insulator materials, common optical dielectrics possess neither of these properties. Here, we demonstrate an optomechanical approach for dynamically suppressing Rayleigh backscattering within dielectric resonators. We achieve this by locally breaking the time-reversal symmetry in a silica resonator through a Brillouin scattering interaction that is available in all materials. Near-complete suppression of Rayleigh backscattering is experimentally confirmed through two independent measurements-the elimination of a commonly seen normal-mode splitting or "doublet" effect and by measurement of the reduction in intrinsic optical loss. Additionally, a reduction of the back-reflections caused by disorder is also observed. Our results provide new evidence that it is possible to dynamically suppress Rayleigh backscattering within any optical dielectric medium using time-reversal symmetry breaking, for achieving robust light propagation in spite of scatterers or defects. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement