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 ^ { -1 } , 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 ( \sim 0.1 pc ) of NGC 6334 V towards the higher-density hot core region ( \sim 0.02 pc ) through two distinctive converging flows dragging the magnetic field , whose strength seems to have been overcome by gravity .