Data on excitation of rare gases is mainly important in the study of lighting, plasma displays and lasers. From literature, cross sections data on electron impact excitation of low-lying resonance states of xenon atoms with both relativistic and non-relativistic computations often differ with available experimental data mostly at low and intermediate impact energies and at intermediate scattering angles. With this in view, we have applied relativistic effects in a fully relativistic distorted-wave born approximation approach to excitation of the lowest lying resonance states of a xenon target atom in a complex potential in order to solve the Dirac equations to obtain the free electron wavefunctions and corresponding excitation cross sections. Present differential cross sections (DCS) results from this study predict that absorption effects in the distortion potential generally have minimal effect on cross sections at impact energies below 50 eV, but then significantly improve these results in comparison with experiments as kinetic energy of the incident electron increases. Furthermore, it is evident that the energy dependent dynamic polarization potential adopted plays a major role in improving shapes of cross sections at low and near threshold impact energies, where other distorted-wave methods fail to give satisfactory results.