Low-noise lasers are a powerful tool in precision spectroscopy, displacement measurements, and development of advanced optical atomic clocks. While all applications benefit from lower frequency noise and robust design, some of them also require lasing at two frequencies. Here, we introduce a simple dual-frequency laser leveraging a ring fiber cavity exploited both for self-injection locking of a standard semiconductor distributed feedback (DFB) laser and for generation of Stokes light via stimulated Brillouin scattering. In contrast to the previous laser configurations, the system is supplied by a low-bandwidth active optoelectronic feedback. Importantly, continuous operation of two mutually locked frequencies is provided by self-injection locking, while the active feedback loop is used just to support this regime. The fiber configuration reduces the natural Lorentzian linewidth of light emitted by the laser at pump and Stokes frequencies down to 270 Hz and 110 Hz, respectively, and features a stable 300-Hz-width RF spectrum recorded with beating of two laser outputs. Translating the proposed laser design to integrated photonics will dramatically reduce cost and footprint for many laser applications such as ultra-high capacity fiber and data center networks, atomic clocks, and microwave photonics.