The afternoon began in Villa's favour and the visiting side appeared strongest for the first spell. John McGinn opened the scoring after 17 minutes, but Tyrick Mitchell earned his first assist when Christian Benteke headed home an equaliser a while later.
Just minutes after Palace pulled level, however, the Villans again took the lead - this time through Anwar El Ghazi striking from range.
Palace then looked dominant in the second-half and enjoyed a prolonged period in their guests' half, testing Villa's backline and 'keeper repeatedly.
Eventually, their efforts paid off and Wilfried Zaha cannoned home before Mitchell bagged his first professional goal minutes from full-time.