The Foxes fought back to level the game before QPR scored a fortunate winner five minutes from the end to record their first away win of the season.
City went close inside 30 seconds of the start when Mark De Vries was inches from getting his head to Momo Sylla's cross.
But it was the Hoops who took the lead on 12 minutes when Marc Nygaard rose above the statuesque Leicester defence to head home a Lee Cook free-kick.
It was the Danish international's first goal for QPR since signing in the summer from Italian side Brescia.
The game took an ugly twist after 21 minutes when a melee broke out involving all 22 players after Maybury had kicked out at Paul Furlong after the pair had challenged for the same ball.
When the dust settled Maybury was shown a straight red card for violent conduct while City's Patrick McCarthy and Rangers' Paul Furlong were handed yellows.
Then just before the break Nygaard had the chance to put Rangers two up but fired over from 15 yards with only the keeper to beat.
After the restart Joey Gudjonsson tested Simon Royce from 25 yards while at the other end Georges Santos headed a Cook cross just over.
There was then a lengthy stoppage while Matthew Hislop needed lengthy treatment before being stretchered off following a clash with Sylla.
The disruption appeared to unsettle QPR who moments after the game had resumed conceded an equaliser.
Leicester substitute Elvis Hammond seized on a De Vries flick before surging into the penalty area and crashing a ten-yard drive beyond Royce. The keeper then denied Hammond a second goal with a spectacular fingertip save.
But five minutes from the end City were dealt a blow when Rangers recaptured the lead when Nygaard's throughball found Furlong whose miscued shot from ten yards wrong-footed Rab Douglas sending the ball spinning into the back of the net.
There was final drama in stoppage time when Furlong was sent off after he was shown a second yellow card following an off-the-ball incident with Gudjonsson.