Away from home at Imperial College's Heston Sports Ground, the Eagles lead after the game's first hour to net three times before losing their focus and allowing a resilient Hoops side to fight their way back into the game.
The home team opened the day's scoring when Stathis Kalathias converted from the spot to give Rangers an early lead. However, shorly after, Sean Robertson bagged Palace's first when he netted in the 25th minute.
It was to be an opening half where the lead was again regained by QPR though, and Lemar Griffiths doubled the Hoops' tally when he netted before half-time.
A flash of goals within three minutes of one another then seemed to have secured all the points for the Eagles as an in-form Brandon Aveiro and Pierrick Keutcha scored just either side of the game's hour mark to make the score 3-2.
However, Paul Furlong's side were not be defeated and just minutes from time, trialist Franklin Domi brought the home team level before Griffiths nabbed his second of the day to finish the R's comeback and earn three points for west London.
The win was QPR's fourth from five and leaves Palace eighth in the table. They will face Cogenhoe United in the FA Youth Cup on Thursday.
Palace: Luthra, D.Boateng, Chamberlin-Gayle, M.Boateng, Russell, Onoabhagbe, Robertson, Donkin (Keutcha 45), Street (Ajayi 70), Averio, Addy.
Subs not used: Whitworth, Gurung, Parris.
QPR: Cooper, McLean (Duberry 75), Pitblado, Kalathias, Mahorn, Kargbo, Paiva, Conte (Payne 75), Griffiths, Grant (Aoraha 46), Domi.