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.
Source: PA
Source: PA