Burnley found themselves ahead after just 90 seconds when Sam Vokes scored from an early counter-attack.
Vokes then became provider just 13 minutes later as he played in Johann Berg Gudmundsson to score his first Burnley goal.
In order to get back into the game, Pardew brought on subsitute Connor Wickham who scored with his first touch of the game.
Palace then got themselves level when Matt Lowton handballed an Andros Townsend cross and Christian Benteke scored from the spot.
Deep into injury time, Burnley got themselves ahead once again when Ashley Barnes rifled home, taking the Clarets up to ninth in the Premier League.