Mars has lost most of its initial water to space as atomic hydrogen and oxygen. Spacecraft measurements have determined that present-day hydrogen escape undergoes large variations with season that are inconsistent with long-standing explanations. The cause is incompletely understood, with likely contributions from seasonal changes in atmospheric circulation, dust activity and solar extreme ultraviolet input. Although some modelling and indirect observational evidence suggest that dust activity can explain the seasonal trend, no previous study has been able to unambiguously distinguish seasonal from dust-driven forcing. Here we present synoptic measurements of dust, temperature, ice, water and hydrogen on Mars during a regional dust event, demonstrating that individual dust events can boost planetary H loss by a factor of five to ten. This regional storm occurred in the declining phase of the known seasonal trend, establishing that dust forcing can override this trend to drive enhanced escape. Because similar regional storms occur in most Mars years, these storms may be responsible for a large fraction of Martian water loss and represent an important driver of Mars atmospheric evolution.