Andre Dozzell was sent off as QPR were beaten by the Championship leaders – their six consecutive defeat.
After Stephy Mavididi opened the scoring, Dozzell equalised shortly before the interval but was dismissed early in the second half.
Struggling Rangers, who remain one off the bottom of the table, battled hard.
But the visitors eventually made their numerical advantage count on 80 minutes, working the ball to Harry Winks, who made space for the shot and rifled in a right-footed strike from near the edge of the penalty area.
QPR have won just once at home in more than a year and have lost all but one of their seven home games this season.
Their spirited showing might somewhat ease the pressure on Gareth Ainsworth, but if he is retained then a defeat away to fellow strugglers Rotherham next weekend would put his future as R’s boss in serious doubt.
Leicester dominated possession from the start and QPR had an early let-off when Cesare Casadei missed a great chance for the Foxes by heading over from six yards out after being found by Kiernan Dewsbury-Hall’s corner.
However, luck went against Rangers when they went behind on the half-hour mark.
Mavididi cut in from the left and Albert Adomah’s attempt to block the shot resulted in a looping deflection off the veteran wide-man, beyond keeper Asmir Begovic and in off the far post.
QPR responded well to that setback and equalised five minutes before half-time.
Lyndon Dykes’ header from Adomah’s cross was cleared off the line by Hamza Choudhury but the ball dropped to Dozzell, who fired home left-footed from near the edge of the penalty area.
But Dozzell went from hero to villain when he was sent off on 59 minutes for two bookable offences.
Abdul Fatawu reacted angrily to a challenge from Dozzell, who raised a hand towards the Leicester winger and was given a yellow card for that retaliation and another for the foul.
It reduced QPR to 10 men for the second successive match, with Jimmy Dunne having been dismissed during the midweek loss at West Brom.
Already without injured centre-backs Steve Cook, Jake Clarke-Salter and Morgan Fox, Dunne’s absence further limited Ainsworth’s defensive options.
Rangers can therefore take some encouragement from the fight they showed against a team that has won 13 of their opening 14 league games this season and are very much on course for promotion.
QPR: Begovic; Cannon, Kakay, Field; Adomah (Smyth 87), Colback (Willock 90), Dozzell, Chair, Paal; Dykes, Kelman (Dixon-Bonner 63).
Subs not used: Archer, Duke-McKenna, Richards, Kolli, Larkeche, Drewe.