A relationship between solar activity and aurorae on Earth was postulated long before space probes directly detected plasma propagating outwards from the Sun. Violent solar eruption events trigger interplanetary shocks that compress Earth's magnetosphere, leading to increased energetic particle precipitation into the ionosphere and subsequent auroral storms. Monitoring shocks is now part of the 'Space Weather' forecast programme aimed at predicting solar-activity-related environmental hazards. The outer planets also experience aurorae, and here we report the discovery of a strong transient polar emission on Saturn, tentatively attributed to the passage of an interplanetary shock--and ultimately to a series of solar coronal mass ejection (CME) events. We could trace the shock-triggered events from Earth, where auroral storms were recorded, to Jupiter, where the auroral activity was strongly enhanced, and to Saturn, where it activated the unusual polar source. This establishes that shocks retain their properties and their ability to trigger planetary auroral activity throughout the Solar System. Our results also reveal differences in the planetary auroral responses on the passing shock, especially in their latitudinal and local time dependences.