We perform a detailed study of the gamma-ray burst GRB 091127/SN 2009nz host galaxy at z = 0.490 using the VLT/X-shooter spectrograph in slit and integral-field unit (IFU) mode. From the analysis of the optical and X-ray afterglow data obtained from ground-based telescopes and Swift-XRT, we confirm the presence of a bump associated with SN 2009nz and find evidence of a possible jet break in the afterglow lightcurve. The X-shooter afterglow spectra reveal several emission lines from the underlying host, from which we derive its integrated properties. These properties agree with those of previously studied GRB-SN hosts and, more generally, with those of the long GRB host population. We use the Hubble Space Telescope and ground-based images of the host to determine its stellar mass (M ). Our results extend to lower M values the M-Z plot derived for the sample of long GRB hosts at 0.3 < z < 1.0 adding new information to probe the faint end of the M-Z relation and the shift of the LGRB host M-Z relation from that found from emission-line galaxy surveys. Thanks to the IFU spectroscopy, we can build the two-dimensional (2D) velocity, velocity dispersion, and star formation rate (SFR) maps. They show that the host galaxy has perturbed rotation kinematics with evidence of a SFR enhancement consistent with the afterglow position.