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Strong discrete aurorae on Earth are excited by electrons, which are accelerated along magnetic field lines towards the planet. Surprisingly, electrons accelerated in the opposite direction have been recently observed. The mechanisms and significance of this anti-earthward acceleration are highly uncertain because only earthward acceleration was traditionally considered, and observations remain limited. It is also unclear whether upward acceleration of the electrons is a necessary part of the auroral process or simply a special feature of Earth's complex space environment. Here we report anti-planetward acceleration of electron beams in Saturn's magnetosphere along field lines that statistically map into regions of aurora. The energy spectrum of these beams is qualitatively similar to the ones observed at Earth, and the energy fluxes in the observed beams are comparable with the energies required to excite Saturn's aurora. These beams, along with the observations at Earth and the barely understood electron beams in Jupiter's magnetosphere, demonstrate that anti-planetward acceleration is a universal feature of aurorae. The energy contained in the beams shows that upward acceleration is an essential part of the overall auroral process.