Neil Warnock's side dominated possession for long periods only to be frustrated by an obdurate Leicester side, who enjoyed a number of opportunities to win the match before Miller's late intervention.
Foxes front two Yakubu and Darius Vassell caused Rangers constant problems, while Andy King and Martyn Waghorn also came close to breaking the deadlock for Sven-Goran Eriksson's men.
The hosts were largely restricted to half chances, with playmaker Adel Taarabt enduring a frustrating afternoon before crucially making way for Miller with four minutes remaining.
QPR's unbeaten run now stands at 11 league games and Swansea's surprise loss at Scunthorpe only served to strengthen their hand in pursuit of the title.
By contrast, play-off chasing Leicester have taken just one point from the last nine on offer.
On-loan Manchester City defender Ben Mee came into the Leicester side for fellow loanee Patrick van Aanholt, the Chelsea youngster sidelined with a thigh injury.
Matt Oakley replaced Paul Gallagher in the visitors' midfield, while QPR were unchanged from the 3-0 win at Middlesbrough last weekend.
Goalmouth action was at a premium in the opening minutes, although Taarabt came in for some predictably rough-house treatment from the Foxes defence.
Leicester goalkeeper Ricardo was finally called into action in the 26th minute when he saved well with his feet from Heidar Helguson after Bradley Orr's long throw had caused confusion in the Leicester box.
Moments later Yakubu collected Darius Vassell's knockdown and his audacious 18-yard lob was impressively clawed behind by Rangers stopper Paddy Kenny.
Jeffrey Bruma rose highest to meet Oakley's corner and Yakubu reacted to smash a volley narrowly over.
Leicester then soaked up a period of QPR pressure before 14-goal midfielder King linked up well with Yakubu and fizzed a 20-yard drive just past Kenny's post.
The Foxes finished the half the stronger of the two sides as Vassell's pace continued to unsettle QPR centre-back Danny Shittu.
Ricardo was the first goalkeeper to be worked in the second half as Buzsaky burst into the box to unleash a 54th minutes shot.
QPR were coming into the ascendancy and Helguson headed narrowly over from a Taarabt free-kick.
Wayne Routledge sprung the Leicester offside trap before firing into the side netting 65 minutes in.
Waghorn came on for Vassell with and should have given Leicester the lead with his first contribution.
The former Sunderland forward beat fellow substitute Matthew Connolly - a first half replacement for the injured Fitz Hall - but lifted over with the goal at his mercy.
Taarabt's frustrating afternoon continued when he dragged QPR's best opportunity wide from 12 yards.
At the other end King rose to meet Yakubu's cross and drew a splendid Kenny save.
Waghorn had another chance with seven minutes remaining but failed to get Yuki Abe's chipped pass out of his feet.
And Leicester were made to rue their profligacy when Miller burst past Sol Bamba to fire past Ricardo with two minutes remaining.
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