Two own goals, the first from Richard Dunne and the second from Steven Caulker in the 95th minute, left the hosts cursing their luck and rooted to the foot of the Premier League table.
Eduardo Vargas had stepped off the bench to give Harry Redknapp’s men hope late on, as he netted either side of a Philippe Coutinho effort, but it was to be Brendan Rodgers celebrating at the final whistle.
He will be a relieved man to be heading home with the points after seeing his side put in a disjointed display in the capital.
Bobby Zamora was a thorn in Liverpool’s side from the off, with the powerful frontman crossing for Leroy Fer to crack the ball off the top of the crossbar just before the half-hour mark.
The Dutchman hit the woodwork again shortly afterwards as he nodded over Simon Mignolet and Glen Johnson had to scramble clear from in front of Charlie Austin and Sandro as the visitors rode their luck.
It appeared destined that the game would end goalless as QPR continued to toil at the start of the second half and Mario Balotelli lifted a volley over a gaping net after Alex McCarthy had parried an effort from Adam Lallana.
A moment of misfortune on 67 minutes brought the contest to life, though, with Johnson latching onto a quickly-taken free-kick to fire across the face of goal and force a disorientated Dunne to poke over his own line.
That was how things stayed until three minutes from time when Austin cushioned a cross fed to the back post into the path of Vargas to volley in from close range.
The tie was suddenly swinging from end to end, with Coutinho finishing off a flowing counter-attack with a low drive that flicked off Caulker before Vargas once again restored parity with a glancing header from a corner which beat Mignolet at his near post before he could claw clear.
Liverpool were not to be denied, though, and as Raheem Sterling raced through, his square pass intended for Balotelli was bundled into an unguarded net by the back-tracking Caulker.
All eyes were on Sterling, in the starting line-up against his old club, after a week in which he had been an almost permanent fixture on the back pages following England manager Roy Hodgson’s revelation that the player had complained of tiredness prior to the qualifier away to Estonia.
Once the game began, there were certainly no signs of fatigue from QPR.
Redknapp has had to fend off suggestions that Les Ferdinand’s arrival as head of football operations puts his Loftus Road status in jeopardy, but this rousing performance points to potential improvements ahead.
Rangers owner Tony Fernandes will be chief among those crossing fingers the club can claim their just rewards in future.
QPR bossed the first half, stretching Liverpool time and again, pulling out all the stops bar a goal.
The hosts outplayed, out-thought and outmanoeuvred lacklustre Liverpool, who had serious problems with Emre Can’s link work with Dejan Lovren and Martin Skrtel.
By contrast Sandro dominated proceedings in front of Rangers’ back line, allowing the likes of Fer to raid effectively off lynchpin Zamora.
Former West Ham striker Zamora was the clear man of the first half, causing untold problems for Can dropping deep to offer the ideal pivot for Rangers’ attacking blueprint.
Fer should have scored twice in the half, so despite all the promise the hosts will have been frustrated to turn around without a comfortable lead.
Austin bundled his way clean through only to bungle his finish, even flicking the rebound wide from Mignolet’s parried save.
Liverpool’s malaise consistently emboldened Rangers, who again should have taken the lead when Zamora drifted into the inside-right berth.
After driving deep into the Liverpool box, Zamora dragged back the perfect ball for the onrushing Fer – only for the Dutchman to blast against the crossbar despite plenty of time and space to pick his spot.
Neither side learned their lesson from the incident, Liverpool allowing Zamora to produce another telling right-wing cross only minutes later.
This time Fer beat Mignolet to the centre and headed goalwards, but again his finish was mere paintwork away from breaking the deadlock.
Liverpool finally conjured a serious opening as the half dwindled to a close, Balotelli’s slide-rule pass inviting Steven Gerrard to tiptoe around Caulker.
The former England skipper’s curling shot was always heading wide however, leaving both sides frustrated at the break, though for vastly differing reasons.
So nearly the home hero, Vargas ought to have cherished getting off the scoring mark in style, but was left to bemoan a strange quirk of fate.
After Dunne put through his own net, all bedlam broke loose, and in the event the hosts were cruelly and unjustly denied.