Segmental relaxations in the neat components and the blend of poly(4-vinylphenol) (PVPh) with poly(ethylene-co-vinyl acetate) (EVA, with 70 wt % vinyl acetate) are studied by broadband dielectric spectroscopy at different temperatures and hydrostatic pressures (up to 750 MPa). Pressure retards the relaxation, with a consequent increase of the glass transition temperature (T-g). The pressure coefficient of T-g is 158 C/GPa for the neat EVA, with temperature and pressure found to exert a comparable effect on segmental relaxation. The shape of the EVA segmental relaxation function, however, is the same for different temperature-pressure conditions at a given relaxation time. On the other hand, PVT measurements on PVPh indicate that temperature is more important than pressure in determining the segmental relaxation time, due to the presence of strong hydrogen bonding. For blends with 20% and 30% PVPh, similar pressure-dependent increases of T-g are observed, although contributions from T and P to segmental relaxation are again comparable, despite the hydrogen bonding between PVPh and EVA. Although both high pressure and temperature reduce the concentration of hydrogen bonds in the blends, which tends to decouple the components' segmental relaxation processes, the relaxation time distribution in the blends is narrowed with increasing pressure at a given relaxation time. This behavior is interpreted by considering the additional mobility achieved from breaking hydrogen bonds at high pressures and high temperatures for the hydrogen-bonded (and thus slow) PVPh-EVA segments compared with the fast relaxation of unassociated EVA segments.