A palladium (Pd) nanogap-based thin-film has been connected to an electrically stable amorphous InGaZnO thin-film transistor, to form a hydrogen sensor demonstrating a dramatic sensing capability. As a result of the Pd connection to the transistor source, our sensor circuit greatly enhances the hydrogen-induced signal and sensing speed in the sense of output voltage, clearly resolving a minimum hydrogen content of 0.05%. When the nanogap-based Pd thin-film was connected to the transistor gate, an extremely limited hydrogen content of even less than 0.05% was visibly detected through gate voltage shifts. Our results exhibit the most promising and practical ways to sense extremely limited hydrogen contents, originating from two methods: transistor-to-Pd nanogap resistor and transistor-to-Pd nanogap capacitor coupling.