The discovery of unconventional superconductivity in a broad class of iron-based materials invoked extensive research on the corresponding compounds of other transition metals. For instance, BaNi2P2 exhibits a superconducting transition with a critical temperature Tc = 2.5 K, and is isostructural to the 122 families of the iron arsenides, suggesting that this Ni-based compound may be another example of unconventional superconductivity. Here we report a detailed analysis of the high-pressure behavior of the angle-and magnetic field-dependent electrical resistivity. The experimentally observed decrease of Tc under the applied pressure matches well with the theoretical prediction based on Migdal-Eliashberg theory, providing evidence in favor of a conventional nature of superconductivity in the nickel analogs of the iron superconductors.