A two-dimensional (2D) Ga2O3 monolayer with an asymmetric quintuple-layer configuration was reported as a novel 2D material with excellent stability and strain tunability. This unusual asymmetrical structure opens up new possibilities for improving the selectivity and sensitivity of gas sensors by using selected surface orientations. In this study, the surface adsorptions of nine molecular gases, namely, O2, CO2, CO, SO2, NO2, H2S, NO, NH3, and H2O, on the 2D Ga2O3 monolayer are systematically investigated through first-principles calculations. The intrinsic dipole of the system leads to different adsorption energies and changes in the electronic structures between the top- and bottom-surface adsorptions. Analyses of electronic structures and charge transport calculations indicate a potential application of the 2D Ga2O3 monolayer as a room-temperature NO gas-sensing device with high sensitivity and tunable adsorption energy using plenary strain-induced lattice distortion.