In this work, WO₃/TiO₂ core–shell (C-S) nanowires (NWs) were successfully synthesized by the coaxial electrospinning method and subsequent high-temperature calcination treatment. After some microscopic structural characterizations, although the prepared WO₃–TiO₂ and TiO₂–WO₃ C-S NWs displayed quite different surface morphologies, both of the shell coatings were uniform and their typical shell thicknesses were extremely close, with mean values of 22 and 20 nm, respectively. In gas sensing tests, WO₃/TiO₂ C-S NWs exhibited good selectivity towards triethylamine (TEA) without significant interfering gases. Compared with bare WO₃ and TiO₂ NWs, WO₃/TiO₂ C-S NWs showed better gas sensing performance. Specifically, the optimal operating temperature and response of TiO₂–WO₃ C-S NWs to 100 ppm TEA were 130 °C and 106, which were reduced by 70 °C and increased by 5.73 times compared to bare WO₃, respectively. Obviously, the C-S nanostructures contributed to improving the gas sensing performance of materials towards TEA. Finally, some hypothetical sensing mechanisms were proposed, which were expected to have important reference significance for the design of target products applied to TEA sensing.