H₂S is a toxic and corrosive gas, whose accurate detection at sub-ppm concentrations is of high practical importance in environmental, industrial, and health safety applications. Herein, we propose a chemiresistive sensor device that applies a composite of single-walled carbon nanotubes (SWCNTs) and brominated fullerene (C₆₀Br₂₄) as a sensing component, which is capable of detecting 50 ppb H₂S even at room temperature with an excellent response of 1.75% in a selective manner. In contrast, a poor gas response of pristine C₆₀-based composites was found in control measurements. The experimental results are complemented by density functional theory calculations showing that C₆₀Br₂₄ in contact with SWCNTs induces localized hole doping in the nanotubes, which is increased further when H₂S adsorbs on C₆₀Br₂₄ but decreases in the regions, where direct adsorption of H₂S on the nanotubes takes place due to electron doping from the analyte. Accordingly, the heterogeneous chemical environment in the composite results in spatial fluctuations of hole density upon gas adsorption, hence influencing carrier transport and thus giving rise to chemiresistive sensing.