Harry Redknapp's newly promoted side begin their campaign against Hull City on August 16, and rounded off preparations for their return to the top flight in disappointing fashion on Saturday.
QPR bossed the vast majority of the first half at Loftus Road, but it was a different story after the break as their Greek opponents took charge.
And veteran defender Hill was the man who gave the visitors the win when he turned Facundo Pereyra's cross past Robert Green after 67 minutes.
QPR began the game brightly, with debutant Jordon Mutch, Shaun Wright-Phillips and Charlie Austin linking up well.
Mutch had the hosts' first real effort on goal after five minutes, turning a PAOK defender before firing wide.
Wright-Phillips was clearly in the mood, wreaking havoc down QPR's right wing, and he drilled wide just after the half-hour mark before feeding Austin in the area, only for the former Burnley man to be crowded out.
PAOK turned the tide after the interval, though, and QPR first needed Green and then the woodwork to keep Stefanos Athanasiadis from putting the visitors ahead early in the second half.
But PAOK did not have to wait long to go in front, as Hill inadvertently diverted Pereyra's centre past his own keeper.
Karl Henry and Austin went closest to equalising for Redknapp's men, but PAOK held firm.