H2D+ is a primary ion that dominates the gas-phase chemistry of cold dense gas. Therefore, it is hailed as a unique tool in probing the earliest, prestellar phase of star formation. Observationally, its abundance and distribution is, however, just beginning to be understood in low-mass prestellar and cluster-forming cores. In high-mass star-forming regions, H2D+ has been detected only in two cores, and its spatial distribution remains unknown. Here, we present the first map of the ortho-H2D+ J(k+, k-) = 1(1,0) -> 1(1,1) and N2H+ 4-3 transition in the DR21 filament of Cygnus X with the James Clerk Maxwell Telescope, and N2D+ 3-2 and dust continuum with the Submillimeter Array. We have discovered five very extended (<= 34,000 AU diameter) weak structures in H2D+ in the vicinity of, but distinctly offset from, embedded protostars. More surprisingly, the H2D+ peak is not associated with either a dust continuum or N2D+ peak. We have therefore uncovered extended massive cold dense gas that was undetected with previous molecular line and dust continuum surveys of the region. This work also shows that our picture of the structure of cores is too simplistic for cluster-forming cores and needs to be refined: neither dust continuum with existing capabilities nor emission in tracers like N2D+ can provide a complete census of the total prestellar gas in such regions. Sensitive H2D+ mapping of the entire DR21 filament is likely to discover more of such cold quiescent gas reservoirs in an otherwise active high-mass star-forming region.