The Eagles had to battle back from Keith Treacy firing North End into the lead, but goals from Neil Danns, Darren Ambrose and Calvin Andrew sealed a deserved victory for Paul Hart's side.
Only 40 seconds had been played when Stern John went close to giving the home side the lead but his lob just crept over the crossbar.
Preston's eighth-minute opener came from a breakaway after Paddy McCarthy's header had been cleared off the line by Neil Mellor, but Shaun Derry was left holding his head in his hands after his mistake was punished.
The Eagles captain was dispossessed and Paul Coutts slipped the ball into the path of Treacy.
The North End winger produced a composed finish past Julian Speroni to claim his first goal for the visitors.
The home side went close to an equaliser in the 18th minute but Andrew's header from a Ambrose corner crashed off the bar.
Jon Parkin wasted a good chance for Preston as he lashed a shot over from Mellor's knock down, before Palace deservedly hauled themselves back onto level terms five minutes before the break.
Preston failed to deal with Andrew's cross and Sean Scannell headed the ball to Danns, who took a touch before firing the ball through the legs of Andy Lonergan from eight yards out for his ninth strike of the campaign.
Palace should have been awarded a penalty in time added-on in the first half when Elliott Ward handled inside the box but referee Roger East did not punish the Preston defender.
Ambrose's 19th goal of the campaign came in the 51st minute. Darren Carter was unable to clear Dann's cross and the Eagles' top-scorer cracked a right-foot volley off the underside of the bar.
Only a smart save from Lonergan prevented Palace from moving further ahead on the hour as he raced out to block Andrew, who had been put clean through by a delightful pass by Ambrose.
Matthew James was close to an equaliser as his shot from the edge of the box just cleared the bar but in the 84th minute the home side made it 3-1 as Andrew knocked the ball in when Lonergan failed to deal with a looping Ambrose cross.
Treacy's 20-yard free-kick was palmed over by Speroni with three minutes of normal time remaining.