Four successive defeats had left City's play-off challenge on a knife edge but they returned to winning ways at the Walkers Stadium.
Leicester maintain their place in the top six and leave QPR with plenty of work still to do to achieve Championship security.
Any nerves City may have had were settled when Wales international Andy King struck after just five minutes.
Paul Gallagher's deep cross from the right was nodded down by Steven Howard for King to drill the ball home from five yards.
Wayne Brown foiled the visitors' first serious assault with a great covering tackle after Adel Taarabt had freed Lee Cook inside the box.
Rangers threatened again when Jay Simpson latched onto a long clearance before feeding Taarabt, whose 16-yard shot extracted a sprawling save from Chris Weale.
Taarabt then strode forward for a shot on goal which was comfortable dealt with by Weale.
The Londoners continued to press and went close on 43 minutes when Simpson hooked the ball over the bar from a good position in front of goal.
Rangers may have dominated first half possession but they found themselves two goals down at half-time courtesy of a blunder by keeper Carl Ikeme.
Brown's long ball forward was chased down by Jay Spearing forcing the advancing keeper into a hurried clearance which fell to Martyn Waghorn, who lifted the ball into an unguarded net from 35 yards.
City raced into a three-goal lead on 50 minutes with a superb strike from the excellent Waghorn.
Richie Wellens won possession in midfield and played the ball forward to Waghorn, who curled a left-foot shot into the top corner from 20 yards.
Weale was called into action on the hour mark when he reacted smartly to block Taarabt from seven yards.
Waghorn, in search of his hat-trick, then struck a 20-yard free kick against the bar before his 16-yard drive was clawed away by Ikeme.
Rangers were denied a consolation goal on 75 minutes when Taarabt stepped inside Brown and drove an 18-yard shot against the outside of a post.
Leicester went 4-0 up on 77 minutes and Michael Morrison dinked in a cross for Howard to flick home a header from six yards.
Howard missed a great chance to make it five for the Foxes in time added on when he headed a Morrison cross tamely at the keeper.