United headed to Loftus Road still harbouring slim hopes of a top-six finish.
That looked even more unlikely after just 27 seconds when Heidar Helguson tapped Rangers ahead.
But Max Gradel hauled Leeds level when he lobbed Radek Cerny and Ross McCormack sealed a 2-1 win with a deflected shot in the second half.
However, Nottingham Forest's win at Crystal Palace means another season outside the top flight for Grayson's men.
"Obviously we are disappointed not to make the play-offs," said Grayson. "We have beaten the champions twice this season which is a testament to my players, but congratulations to QPR."
Source: PA