Shaun Wright-Phillips, an early substitute for the injured Junior Hoilett, struck a brilliant 78th-minute winner against the club he left in 2008 to further erode the Blues' fading title hopes.
Rangers defended resolutely throughout and created more chances to score in an entertaining second half.
It was a crucial victory that ended their three-match losing run, giving Harry Redknapp his second win since becoming manager last month, and while they remain bottom of the table on goal difference the result invigorated their relegation battle.
The lack of a goal will have added urgency to Chelsea's pursuit of Demba Ba after today tabling the £7million bid that has triggered the release clause in the Newcastle striker's contract.
Marko Marin, making his first start, was extremely lucky to escape a fourth-minute red card from referee Lee Mason after driving into the shin of Stephane Mbia with a one-footed, studs-first challenge.
QPR suffered a setback when Hoilett limped off in the 16th minute with what appeared to be a hamstring problem, resulting in Wright-Phillips' arrival from the bench.
David Luiz directed an attempt into the ground and onto the top netting and Chelsea threatened again shortly after when Branislav Ivanovic outmuscled Adel Taarabt and drove into the box, finding Marin who gave the ball away.
A corner bounced harmlessly off the shin of Torres and play quickly swept to the opposite end as Esteban Granero picked out Wright-Phillips from long range, with the ensuing first-time shot slipping narrowly wide.
QPR rarely escaped their half but were defending resolutely with skipper Clint Hill nodding clear a curling shot from Oscar.
The Blues lost their way in the 10 minutes before half-time, the result of a lack of urgency and series of errors, but shots from Oscar and Frank Lampard brought them back to life.
Moses wasted a glorious chance three minutes after the interval when he steered Marin's fast pass wide when only four yards out.
QPR's goal was coming under growing pressure with Ivanovic grazing the crossbar, Luiz seeing a rocket blocked and only a brave save by Julio Cesar denying Torres from point-blank range.
Lampard then stabbed the ball home but the flag had been raised for offside in what was a close but correct call.
Once again Chelsea faded and this time QPR took advantage, working the ball from a corner via Taarabt to Wright-Phillips, who drove the ball into the bottom left corner of the net from the edge of the area.
Ivanovic nodded over the crossbar in the dying moments and QPR held on for a precious three points.