We have studied the young low-mass pre-main sequence (PMS) stellar population associated with the massive star-forming region DR 21 by using archival X-ray Chandra observations and by complementing them with existing optical and infrared (IR) surveys. The Chandra observations have revealed for the first time a new highly extincted population of PMS low-mass stars previously missed in observations at other wavelengths. The X-ray population exhibits three main stellar density peaks, coincident with the massive star-forming regions, being the DR 21 core the main peak. The cross-correlated X-ray/IR sample exhibits a radial 'Spokes-like' stellar filamentary structure that extends from the DR 21 core towards the northeast. The near-IR data reveal a centrally peaked structure for the extinction, which exhibits its maximum in the DR 21 core and gradually decreases with the distance to the N-S cloud axis and to the cluster centre. We find evidence of a global mass segregation in the full low-mass stellar cluster, and of a stellar age segregation, with the youngest stars still embedded in the N-S cloud, and more evolved stars more spatially distributed. The results are consistent with the scenario where an elongated overall potential well created by the full low-mass stellar cluster funnels gas through filaments feeding stellar formation. Besides the full gravitational well, smaller scale local potential wells created by dense stellar sub-clusters of low-mass stars are privileged in the competition for the gas of the common reservoir, allowing the formation of massive stars. We also discuss the possibility that a stellar collision in the very dense stellar cluster revealed by Chandra in the DR 21 core is the origin of the large-scale and highly energetic outflow arising from this region.