Andros Townsend sent Palace into half-time with a one goal lead, after a brilliantly worked move between Patrick van Aanholt and Wilfried Zaha.
Liverpool struck back twice within seven minutes of the second half with goals from Mohamed Salah and Roberto Firmino, before James Tomkins levelled the scoreline.
Salah pounced to score his second and Liverpool's third, before Sadio Mane struck a fourth in the 93rd minute. But Max Meyer narrowed the gap with his first goal for Palace in the dying seconds, as the Eagles were defeated 4-3.
Watch extended highlights of a thrilling game on Merseyside now on Palace TV for free, on the club's official app or by clicking here if you are viewing on desktop.