© PA Photos
The hosts had a great chance to take the lead when David Meyler brought down Dean Moxey in the box and a penalty was awarded.
However, Glenn Murray saw his spot kick saved by Stockdale to keep the scores level.
Ian Holloway's side were given another penalty in stoppage time as Murray's shot hit the arm of a Tigers defender.
Kevin Phillips dispatched the spot kick despite Stockdale getting a hand to his shot.
Palace doubled their lead when Phillips got his second of the night in slightly fortuitous circumstances as he miskicked the ball onto his left foot and the effort beat Stockdale and landed in the corner of the net.
It was three for Holloway's side and Phillips who bagged his hat-trick as he fired his shot over Stockdale with the aid of a deflection into the top corner.
Hull got a goal back as Jay Simpson's looping header drifted over Julian Speroni and found the net.
Palace restored their three-goal cushion when Zaha beat Paul McShane following a neat one-two and slotted the ball past Stockdale.
The visitors scored a late consolation goal as David Meyler headed past Speroni from Robbie Brady's free kick.