An own goal by goalkeeper Lee Camp was all that separated Premier League high-flyers from their Championship opposition.
Bereft of many star performers, Chelsea's bit players came to the fore sporadically, specifically Claudio Pizarro who earned the win when his speculative strike in the first half rebounded off the hapless Camp and into the net
The game started brightly for the visitors, so much that only some desperate defending by Chelsea prevented QPR from making an early breakthrough.
But some classy interchange by the home side on 11 minutes saw Ashley Cole zip the ball across and full-back Chris Barker did well to hack away for a corner
A limp left-footed shot by Paulo Ferreira on 23 minutes from 25 yards which trickled wide of Camp's goal was the home side's first shot on goal.
But with their second shot on 28 minutes they scored when a ball by Ashley Cole fed Pizarro on the edge of the penalty area.
The Peruvian striker let rip with a low right footer which ricocheted off Camp's right upright and bounced off the hapless goalkeeper's arm and back into his empty net.
Shaun Wright-Phillips' mazy run and shot on 39 minutes threatened to raise the game from its stupor, but the England winger's powerful drive flew just over Camp's crossbar.
For QPR's part, their first shot towards goal came on 43 minutes from the wayward strike of midfielder Akos Buzsaky, but his left footer from 30 yards sailed high and wide of Hilario's goal.
Chelsea could have doubled their lead seconds from the break when a sweeping move saw Steve Sidwell unload a 25-yarder which smacked off Camp's right post and out to safety.
Brazilian Alex had a fine 35-yard free-kick saved by Camp on 46 minutes.
Martin Rowlands almost sent the away fans into delirium on 50 minutes, but his fine left-footed half-volley from just outside the area was inches above the Chelsea crossbar.
He followed his up with another fine strike five minutes later and this time the ball was on target, but Hilario dealt with it comfortably.
Rangers piled on the pressure and Dexter Blackstock's shot was charged down by Alex and held by Hilario.
Didier Drogba returned to action for the first time in a month in place of Scott Sinclair on 60 minutes.
But the game fizzled out with QPR unable to muster a worthwhile challenge while Chelsea were happy to play out time.