Intense rainfall events significantly affect Alpine and Alaskan glaciers through enhanced melting, ice-flow acceleration and subglacial sediment erosion, yet their impact on the Greenland ice sheet has not been assessed. Here we present measurements of ice velocity, subglacial water pressure and meteorological variables from the western margin of the Greenland ice sheet during a week of warm, wet cyclonic weather in late August and early September 2011. We find that extreme surface runoff from melt and rainfall led to a widespread acceleration in ice flow that extended 140 km into the ice-sheet interior. We suggest that the late-season timing was critical in promoting rapid runoff across an extensive bare ice surface that overwhelmed a subglacial hydrological system in transition to a less-efficient winter mode. Reanalysis data reveal that similar cyclonic weather conditions prevailed across southern and western Greenland during this time, and we observe a corresponding ice-flow response at all land- and marine-terminating glaciers in these regions for which data are available. Given that the advection of warm, moist air masses and rainfall over Greenland is expected to become more frequent in the coming decades, our findings portend a previously unforeseen vulnerability of the Greenland ice sheet to climate change.