The change in phase stability of Group-VB (V, Nb, and Ta) transition metals due to pressure and alloying is explored by means of first-principles electronic-structure calculations. It is shown that under compression stabilization or destabilization of the ground-state body-centered cubic (bcc) phase of the metal is mainly dictated by the band-structure energy that correlates well with the position of the Kohn anomaly in the transverse acoustic phonon mode. The predicted position of the Kohn anomaly in V, Nb, and Ta is found to be in a good agreement with data from the inelastic x-ray or neutron scattering measurements. In the case of alloying the change in phase stability is defined by the interplay between the band-structure and Madelung energies. We show that band-structure effects determine phase stability when a particular Group-VB metal is alloyed with its nearest neighbors within the same d-transition series: the neighbor with less and more d electrons destabilize and stabilize the bcc phase, respectively. When V is alloyed with neighbors of a higher (4d- or 5d-) transition series, both electrostatic Madelung and band-structure energies stabilize the body-centered-cubic phase. The opposite effect (destabilization) happens when Nb or Ta is alloyed with neighbors of the 3d-transition series.