Hydrogen, the lightest and most abundant element in the universe, holds immense importance across various fields of application from industry to healthcare. Detecting hydrogen is crucial in medical diagnostics and leak detection, as it helps diagnose gastrointestinal conditions and ensures safety in industrial settings by identifying potential leaks in hydrogen-based systems. In this study, we present the synthesis of tin oxide (SnO/SnO2) nanosheets using a facile hydrothermal method followed by the decoration of Pd-Ag alloy nanoparticles (NPs) for the purpose of hydrogen gas detection. Different combinations of Pd and Ag in Pd-Ag alloy NPs were tested on the surface of the SnO/SnO2 nanosheets in order to optimize their catalytic properties for enhanced hydrogen gas sensing. The Pd-Ag alloy NPs with a ratio of 1:0.5 decorated on SnO/SnO2 nanosheets (Pd1Ag0.50@SnO/SnO2), exhibited the highest response (s = Ra/Rg) of 81.34 at an optimum temperature of 225 °C compared to the bare SnO/SnO2 nanosheets. The fabricated sensor also showed an excellent level of selectivity, repeatability, and a good response time (45 s). The enhanced sensing response of Pd1Ag0.50@SnO/SnO2 towards hydrogen is explained using the spillover and electronic sensitization mechanism. The combined gas sensing mechanism is discussed in detail.