Palace had the perfect start, Zaha pouncing on mistakes in the Hull defence to score after only three minutes.
The Eagles doubled their lead on 34 minutes when Benteke rose highest to head home from Jason Puncheon's corner.
Hull had plenty of the ball in the second half but they did not really threaten and Milivojevic made it 3-0 with an 85th-minute penalty while Van Aanholt completed the scoring in the final minute.
The Tigers join Middlesbrough and Sunderland in dropping to the Championship and are relegated after a one-season stay in the top flight.
Palace, meanwhile, move up to 13th with 41 points from 37 matches.