Relaxor ferroelectrics, with their strong dependence of polarization on the applied electric field, are of considerable technological importance. On a microscopic scale, however, there exists competition as well as coexistence between short-range and long-range polar order. The conventional picture is that the polar nano-regions (PNRs) that appear at high temperatures beyond the Curie transition, form nuclei for the field-induced long-range order at low temperatures. Here, we report high-energy X-ray diffuse-scattering measurements on the relaxor Pb(Zn1/3Nb2/3) O-3 (PZN) to study the short-range polar order under an electric field applied along the [ 111] direction. In contrast to conventional expectations, the overall diffuse-scattering intensity is not suppressed. On the other hand, the field induces a marked change on the shape of the three-dimensional diffuse-scattering intensity pattern, corresponding to a redistribution of PNRs in real space. We show that these surprising results are consistent with a model in which the PNRs with [ 110]-type polarizations, orthogonal to that of the surrounding environment, are embedded and persist in the [111]-polarized ferroelectric order of the bulk.