Andy King opened the scoring with a tidy finish after five minutes before a calamitous error from Rangers goalkeeper Carl Ikeme gifted Martyn Waghorn the second goal on the stroke of half-time.
Waghorn then netted with a superb strike five minutes after the break to take his tally for the season to 11.
Strike partner Steve Howard completed the scoring when he headed home in the 78th minute.
Leicester made three changes to their starting XI. Wayne Brown replaced Robbie Neilson in defence while Paul Gallacher and Jay Spearing were recalled in midfield at the expense of Lloyd Dyer and Matt Oakley.
QPR's only change saw Lee Cook come in for Tamas Priskin.
The hosts started brightly and went ahead after good work from Gallacher resulted in King sliding the ball into the net from eight yards out following Howard's knock down.
Howard and Waghorn threatened to extend Leicester's lead before Rangers thought they had equalised in the 39th minute.
Mikele Leigertwood's long-range shot deflected in off Jay Simpson, leaving City goalkeeper Chris Weale stranded. However, Simpson was stood in an offside position and the referee's assistant intervened.
Cook then beat Bruno Berner to Alejandro Faurlin's long ball forward and his lobbed effort beat Weale but went over the crossbar.
Ikeme's howler then sent the Foxes into the break in full control.
Ikeme, making the last appearance of his loan spell before returning to Wolves, failed to control a long punt forward outside his area and Waghorn simply rolled the ball into the unguarded net.
The on-loan Sunderland striker scored his second goal of the game after 50 minutes.
He collected the ball on the right and cut infield before curling a left-foot shot in off the underside of the crossbar from the edge of the box.
With a little more luck, Waghorn would have had a hat-trick. First Ikeme atoned for his error by tipping a shot over the crossbar before a free-kick struck the angle of post and crossbar and Ikeme saved Waghorn's second attempt from the rebound.
At the other end, Simpson shot wide before Adel Taarabt clipped the outside of a post with a 25-yard effort.
Howard headed only his fourth goal of the season from Michael Morrison's right-wing cross soon afterwards.