Two second-half goals from Jean-Philippe Mateta, a long-range strike and a late penalty, secured a deserved 2-0 win for the Eagles.
Darwin Nunez came off the bench to score a stoppage-time double.
Fans register their dismay at shocking run as relegation fears deepen at the King Power Stadium
Jean-Philippe Mateta at the double as resurgent Palace seal first London derby away win since 2022