Graeme Lee’s side will travel to Selhurst Park on the weekend of Friday, February 4 to Monday, February 7.
Pools earned their spot in the fourth round following a dramatic win over Blackpool in round three.
Keshi Anderson gave the Championship side an early lead at the Suit Direct Stadium with the Seasiders wasting a number of good opportunities to extend that lead throughout the first half.
But Pools performed heroically after the break finding a way back into the game through David Ferguson’s deflected strike.
And Lee's side completed a stunning turnaround when Joe Grey handed Pools the lead just moments after coming on as a substitute.
Pools were more than a match for their Championship opponents in the second half and were able to hold on to cap another memorable day for the club this season.
Lee’s side have already beaten opposition from League One and the Championship in the FA Cup having overcome Wycombe Wanderers and Lincoln City in rounds one and two and will now get to test themselves against Premier League opposition against Patrick Vieira’s Eagles after they came from behind to beat Millwall.
Pools’ victory over Blackpool earned the club £82,000 taking their total prize money from the competition up to £138,629.
Should Pools claim another win in the competition they will bank an additional £90,000.
As a result of Pools’ success in the FA Cup, the League Two fixture with Mansfield Town, which was originally scheduled for Saturday, February 5, will now be rescheduled.
Elsewhere, Chris Wilder’s Middlesbrough will face either Manchester United or Aston Villa in the fourth round.
Boro avoided a cup upset themselves in round three having been pegged back from two goals to the good against League Two Mansfield.
Uche Ikpeazu gave Boro the lead with a stunning solo goal before Caolan Boyd-Munce doubled their lead with a debut goal.
But Nigel Clough’s Stags staged a spirited comeback when Oli Hawkins headed in from Stephen Quinn’s cross before former Pools striker Rhys Oates grabbed an equaliser five minutes from time.
But with the tie headed towards extra time Boro snatched it as Isaiah Jones sped down the right and his cross was turned into his own net by Elliott Hewitt.