Here, we report the observation of pressure-induced superconductivity in type-II Weyl semimetal (WSM) candidate NbIrTe4 and the evolution of its Hall coefficient (RH), magnetoresistance (MR), and lattice with increasing pressure to ∼63 GPa. These results provide a significant opportunity to investigate the universal high-pressure (HP) behavior of ternary WSMs, including the sister compound TaIrTe4 that has been known through our previous studies. We find that the pressure-tuned evolution from the WSM to the superconducting (SC) state in these two compounds exhibits the same trend, i.e., a pressure-induced SC state emerges from the matrix of the non-SC WSM state at ∼27 GPa, and then the WSM and SC states coexist up to 40 GPa. Above this pressure, an identical HP behavior, characterized by almost the same value of RH and MR in its normal state and the same value of Tc in its SC state, appears in both compounds. Our results not only reveal the evolution from the WSM state to the SC state but also demonstrate that NbIrTe4 and TaIrTe4 can make the same contribution to the normal and SC states that inhabit the HP phase, although these two compounds have dramatically different band structure at ambient pressure.