Auroras ('northern lights') glow differently on each planet. Earth’s main auroras form a wide oval ring, powered by particles from the Sun. Saturn’s auroras act uniquely: when hit by dense solar particles, its main ring vanishes, replaced by bright lights near its poles. This switch was only seen at Saturn—until now. Our study discovered that during extremely rare moments when the Sun’s particle flow drops to record lows near Earth, our planet performs a similar light show. Earth’s familiar auroral ring disappears, and intense, dancing lights emerge close to the North Pole—matching Saturn’s pattern. Surprisingly, this happens without Saturn’s rapid spin or other special conditions. This finding reveals that two very different planets can temporarily 'swap' auroral styles under extreme space weather. It suggests a universal rule may govern auroras across our solar system: when the solar wind becomes unusually strong or weak, planets may flip their auroral displays in predictable ways. By comparing Earth and Saturn, we uncover hidden connections in how worlds respond to the Sun’s influence.