High-temperature β-Ga2O3:Cr2O3-based sensors sensitive to oxygen- and hydrogen-containing gases have been developed and studied. Magnetron cosputtering is the method of choice for the thin film synthesis as an industry-compatible technique. The composition-structure-properties relationship has been revealed. An introduction of 0.04–0.14 wt. % Cr leads to a significant increase in the response of the O2 sensors over the temperature range 250–400 °C. The highest response in the above-mentioned temperature range has been achieved for a Cr addition of 0.14 wt. %. An increase in the Cr content from 0.04 to 0.22 wt. % leads to a decrease in the β-Ga2O3-based sensors’ response time, especially for low O2 concentrations (≤10 vol. %). Reliable control of the β-Ga2O3:Cr2O3-based sensors’ selectivity to industry-relevant reducing gases—hydrogen, carbon monoxide, and toluene—is demonstrated. β-Ga2O3 films with a Cr incorporation content of 0.04 and 0.06 wt. % have a high response to toluene at operating temperatures 300–500 °C, while the films with 0.14 and 0.22 wt. % Cr have a high response to H2 in the range 400–500 °C. Regardless of the Cr content in β-Ga2O3 thin films, all sensors considered demonstrate a weak response to CO within the operating temperature range 250–500 °C. The results attained are of certain technological importance, i.e., in terms of the development of cost-effective methods for the synthesis of materials and systems for monitoring and control of industry-relevant gases for an environmentally friendly and sustainable growth.