The pressure dependent physical properties of Nb-based equiatomic quaternary Heusler alloys NbMnVAl and NbFeCrAl have been investigated using full-potential linearized augmented plane wave (FP-LAPW) method with exchange and correlation potentials of the PBEsol scheme. Half-metallic behavior in NbMnVAl (NbFeCrAl) with band gap of 0.32 (0.29) eV in spin-down (spin-up) state at ambient pressure is observed. The total magnetic moments are derived as 2.0 μΒ/f.u. for NbMnVAl and NbFeCrAl alloys, which reconciles with Slater-Pauling rule. Phonon frequencies are computed using Vienna Ab initio Simulation Package (VASP). The exchange interactions and Curie temperatures are determined using spin-polarized relativistic Korringa-Kohn-Rostoker (SPR-KKR) method. Moreover, the computations of mechanical properties revealed the stability and ductile nature of both compounds. The optical properties proved the applicability of these compounds in optoelectronic devices. Pressure dependent half-metallic properties are discussed to show spintronic applications of both the quaternary alloys.