Large continental earthquakes necessarily involve failure of multiple faults or segments. But these same critically-stressed systems sometimes fail in drawn-out sequences of smaller earthquakes over days or years instead. These two modes of failure have vastly different implications for seismic hazard and it is not known why fault systems sometimes fail in one mode or the other, or what controls the termination and reinitiation of slip in protracted seismic sequences. A paucity of modern observations of seismic sequences has hampered our understanding to-date, but a series of three Mw>6 earthquakes from August to November 2016 in Central Italy represents a uniquely well-observed example. Here we exploit a wealth of geodetic, seismological and field data to understand the spatio-temporal evolution of the sequence. Our results suggest that intersections between major and subsidiary faults controlled the extent and termination of rupture in each event in the sequence, and that fluid diffusion, channelled along these same fault intersections, may have also determined the timing of rupture reinitiation. This dual control of subsurface structure on the stop-start rupture in seismic sequences may be common; future efforts should focus on investigating its prevalence.