Miniature lasers emitting dual-wavelength modes have diverse applications alongside the more explored single-mode counterparts. However, having dual-wavelength modes originating from a plasmonic-photonic hybrid laser is still a relatively new area for research. Compared to the amount of literature devoted to the physics of such hybrid cavities, only a few have analyzed their role in lasing applications. Notably, the role of hybrid cavities in dual-wavelength lasing is still unexplored. In this work, the properties of one-dimensional distributed Bragg reflectors and thin metal nanohole arrays come together to create a hybrid dual-mode plasmonic laser. The similar energy distribution characteristics of photonic and plasmonic lasers make hybrid structures a viable choice for efficient dual-mode lasing. In this work, the lasing cavity simultaneously excites photonic and Tamm plasmonic modes to generate dual-mode lasing. Consequently, the proposed laser shows high emission output with narrow linewidth and a clear and tunable mode separation.