We proposed and experimentally demonstrated a novel scheme of light group velocity control via a Mach-Zehnder fiber interferometer incorporated with Brillouin random lasing resonance in a half-open linear cavity. A theoretical model of the proposed Brillouin random lasing resonance-based Mach-Zehnder interferometer (BRLR-MZI) for the light group velocity manipulation was derived, predicting optical power-dependent transmittance spectrum shift as well as the enhancement of the temporal advancement. Thanks to Brillouin random lasing-induced fast light effect, the proposed scheme not only achieves a flexible all-optical manipulation of its transmittance spectrum but also overcomes the saturation effect for the light speed control based on a traditional MZI. In experimental validation, sinusoidally modulated signals with the modulation frequency of 160 kHz ultimately experienced a maximum advancement of 4031 ns (corresponding to the group index of 0.875), which exhibits an advancement improvement of 1364 ns compared with the traditional MZI-based scheme. It suggests a promising platform for exploring applications in fields of all-optical signal processing, microwave photonic, and ultra-sensitive fiber sensing.