Experimental and theoretical models are used to explore the break of a moraine dam by catastrophic erosional incision initiated by an overtopping wave. The experiments are conducted in a rectangular tank with an erodible barrier made from sand and grit. Theory combines shallow-water hydrodynamics with an empirical model of erosion. The models confirm that dams can be broken by a catastrophic incision. However, the displacement wave does not break the dam in its first passage but excites a long-lived seiche that repeatedly washes over the dam. The cumulative erosion of the downstream face by the overtopping seiches eventually allows an incipient channel to form, and catastrophic incision follows. Estimates are presented of the strength of the initial disturbance required to break the dam, the maximum discharge and the duration of the runaway incision.