We present Submillimeter Array (SMA) observations at 345 GHz towards the intermediate/high-mass cluster-forming region NGC 6334 V. From the dust emission we spatially resolve three dense condensations, the brightest one presenting the typical chemistry of a hot core. The magnetic field (derived from the dust polarized emission) shows a bimodal converging pattern towards the hot core. The molecular emission traces two filamentary structures at two different velocities, separated by 2 km/s, converging to the hot core and following the magnetic field distribution. We compare the velocity field and the magnetic field derived from the SMA observations with MHD simulations of star-forming regions dominated by gravity. This comparison allows us to show how the gas falls in from the larger-scale extended dense core (~0.1 pc) of NGC 6334 V towards the higher-density hot core region (~0.02 pc) through two distinctive converging flows dragging the magnetic field, whose strength seems to have been overcome by gravity.