Fungi from the genera Colletotrichum and Curvularia are listed among the most important air-borne pathogens infecting Brassica plants. The use of biological control agents, such as Streptomyces species, offers an alternative and effective way to reduce airborne pathogens. The aim of this research was to select Streptomyces species with potential for use as biological agents against Colletotrichum sp. and Curvularia lunata, the leaf spot fungi of Tokyo Bekana cabbage, and to assess the mechanisms involved. Dual culture assays showed that all the Streptomyces species inhibited the growth of both fungal pathogens. In particular, Streptomyces angustmyceticus NR8-2 inhibited the growth of Colletotrichum sp. and C. lunata by 75.6% and 69.5%, respectively, which was significantly more than the other isolates. The activity of the cell wall-degrading enzyme β-1,3-glucanase in the cell-free culture filtrate (CF) of S. angustmyceticus NR8-2 was 0.33 U mL−1, and this activity was significantly higher than that of the control. The thermostable antifungal metabolites of the cell-free CF inhibited the mycelia growth of Colletotrichum sp. and C. lunata when tested by the agar diffusion method. Furthermore, solid-phase microextraction GC/MS analysis showed that S. angustmyceticus NR8-2 emitted volatile antifungal compounds, including alcohols, aldehydes, carboxylic acids, and fatty acids. The application of the S. angustmyceticus NR8-2 spore suspension and cell-free culture filtrate reduced the disease severity index of leaf spots. This study demonstrated the production of cell wall-degrading enzymes, heat stable antifungal metabolites and volatile antifungal compounds by S. angustmyceticus NR8-2, and these products are involved in the antifungal activity against Colletotrichum sp. and C. lunata.