The electronic structure, mechanical stability, phonon dispersion and vibrational characteristics of half-Heusler alloys, ScAuX (X = Si, Ge, Sn, Pb) have been analyzed in framework of Density Functional theory(DFT). The alloys are crystallize in face centered cubic having F4‾3m(#216) space group. First-principles simulation reveals that all the alloys are narrow band gap semiconductors. The electronic structure is investigated using generalized gradient approximation under Perdew-Burke-Ernzerhof parameterization(GGA + PBE). To predict the accurate band gap of the compounds, comparatively more refined hybrid functional such as Heyd-Scuseria-Ernzerhof (HSE06) has been taken into account. The calculated elastic constants verify the mechanical stability of all the systems by tolerating Born-Huang criteria. In addition, the phonon dispersion and shear constant also favor in mechanical stability. A detailed investigation of vibrational characteristics have been performed. On the basis of electronic band structure topology and calculated theoretical limit of minimum lattice thermal conductivity, our simulated results predict that all the alloys are promising candidates for thermoelectric applications.