Mars has lost most of its initial water to space as atomic H and O. The H portion of this loss was long thought to be controlled by the O loss via a photochemical feedback cycle that ensures planetary redox neutrality [1,2]. Recent measurements of H loss, dust activity, and middle atmospheric water content have shown that each of these vary strongly with season, suggesting a causal connection between climate cycles that drive dust and H escape [3-10]. However, no prior study has captured the full chain of events leading to H loss. Here we present measurements from the Mars Year 34 regional C storm (Jan-Feb 2019), unambiguously establishing that even regional dust events enhance planetary H loss by a factor of several. Because this storm occurred after perihelion and southern summer solstice in the declining phase of the seasonal trend, these observations allow us to conclude that dust, not season or EUV flux, is responsible for the enhanced escape. Combining dust, ice, and temperature measurements from MRO/MCS, water vapor measurements from TGO/NOMAD and TGO/ACS, and cloud and hydrogen measurements from MAVEN/IUVS allows us to establish the timescale of dust impacts on the water and H abundances of the upper atmosphere. We find that it takes approximately one week for lower atmospheric dust to affect water abundances at 60 km, and an additional week for this water to induce a change in the upper atmospheric H inventory and escape rate.