Neil Warnock's side have been flying and took the lead after only 12 minutes when Adel Taarabt's cross picked out Jamie Mackie and he sent a bullet header past Carl Ikeme.
Leicester thought they should have had a penalty in the second half when Steven Howard appeared to be elbowed but nothing was given - much to the fury of the Foxes players and fans alike.
The home side continued to press for an equaliser but QPR wrapped up victory with four minutes remaining when Mackie beat the challenge of Michael Morrison before firing in his eighth goal of the season.
QPR started full of confidence and Taarabt fizzed a shot from 25 yards straight into the arms of Leicester goalkeeper Ikeme.
However the Foxes went straight up the other end and Martyn Waghorn had a shot superbly blocked by Kaspars Gorkss.
With 12 minutes gone QPR took the lead when Taarabt received the ball on the right and whipped in a fine cross to Mackie who powered in a header.
Leicester reacted well to going behind and Matt Oakley played in Richie Wellens but he sent an angled drive over the bar when perhaps a cross might have been a better option.
On the half-hour mark Gorkss was penalised for handball and Waghorn had a good opportunity from a free-kick 20 yards out only to send a poor effort over the bar.
The home side were playing the better football as the half wore on but were unable to create any meaningful opportunities with Wellens having a shot blocked.
Four minutes before the break, Matt Fryatt got a shot away from close range but QPR goalkeeper Paddy Kenny gathered the effort easily.
Leicester came flying out the traps at the start of the second-half and Fryatt went close with a shot that went just over the bar.
Minutes later Andy King saw a shot comfortably saved by Kenny before the former Sheffield United keeper made a fine stop to deny Fryatt.
The Foxes thought they should have had a penalty when Howard looked to have been elbowed in the box but the referee waved away the claims despite the substitute suffering a bloody nose from the challenge.
The sense of injustice seemed to galvanise Leicester and they continued to press forward with Kenny alert once again to keep out Paul Gallagher's shot.
However despite all their pressure, QPR doubled their lead late on when a quick break saw the in-form Mackie receive the ball and he produced a precise finish.