We demonstrated selective gas sensing with MoS2 thin-film transistors using the change in the channel conductance, characteristic transient time and low-frequency current fluctuations as the sensing parameters. The back-gated MoS2 thin-film field-effect transistors were fabricated on Si/SiO2 substrates and intentionally aged for a month to verify reliability and achieve better current stability. The same devices with the channel covered by 10 nm of Al2O3 were used as reference samples. The exposure to ethanol, acetonitrile, toluene, chloroform, and methanol vapors results in drastic changes in the source-drain current. The current can increase or decrease by more than two-orders of magnitude depending on the analyte. The reference devices with coated channel did not show any response. It was established that transient time of the current change and the normalized spectral density of the low-frequency current fluctuations can be used as additional sensing parameters for selective gas detection with thin-film MoS2 transistors.