We frequency stabilize the output of a miniature stimulated Brillouin scattering (SBS) laser to rubidium atoms in a microfabricated cell to realize a laser system with frequency stability at the 10-11 level over seven decades in averaging time. In addition, our system has the advantages of robustness, low cost and the potential for integration that would lead to still further miniaturization. The SBS laser operating at 1560 nm exhibits a spectral linewidth of 820 Hz, but its frequency drifts over a few MHz on the 1 hour timescale. By locking the second harmonic of the SBS laser to the Rb reference, we reduce this drift by a factor of 103 to the level of a few kHz over the course of an hour. For our combined SBS and Rb laser system, we measure a frequency noise of 4 × 104 Hz2/Hz at 10 Hz offset frequency which rapidly rolls off to a level of 0.2 Hz2/Hz at 100 kHz offset. The corresponding Allan deviation is ≤2 × 10-11 for averaging times spanning 10-4 to 103 s. By optically dividing the signal of the laser down to microwave frequencies, we generate an RF signal at 2 GHz with phase noise at the level of -76 dBc/Hz and -140 dBc/Hz at offset frequencies of 10 Hz and 10 kHz, respectively.