Daniel Shittu's header looked like rescuing a point after Richard Stearman had put the visitors 2-1 up with 12 minutes left, but Leicester – managerless following the recent departure of Craig Levein - hit back to take all three points.
QPR made the perfect start by going ahead after six minutes. Richard Langley picked out Lee Cook whose left-wing cross was headed home by Gareth Ainsworth.
But the lead lasted only four minutes. A mix-up between Shittu and Georges Santos let in Matt Fryatt who fired home from eight yards.
Leicester suffered a set back when Gareth Williams limped off but they continued to put the home side under pressure.
Rangers keeper Simon Royce had to stretch to push Fryatt's cross away from Iain Hume and later produced a good save to keep out Alan Maybury's shot.
QPR failled to improve after the break and Nils-Eric Johansson headed Johannes Gudjonsson's corner over Royce's bar before Maybury sent an effort just over.
QPR boss Ian Holloway sent on teenage striker Shabazz Baidoo in place of Marc Nygaard and briefly his side improved.
Ainsworth netted after Cook's shot deflected into his path but the winger was denied a second goal by an offside flag.
Rangers looked to be finally getting on top but fell behind when Johansson's cross found an unmarked Stearman who gave Royce no chance.
Shittu headed the home side level five minutes later but more poor defending handed Leicester their third of the game soon after.
Gudjonsson beat the offside trap and passed to Hughes who had the simple task of tapping the ball into the empty net.
There was no way back after that for Ian Holloway's team who were booed off at the final whistle by their angry supporters.