A woeful QPR display intensified their relegation fears as they were beaten by a Luis Suarez-inspired Liverpool.
Reds' boss Brendan Rodgers was absent from the game with a bug but Suarez twice capitalised on poor defending to put the visitors 2-0 ahead.
QPR were denied a penalty when Adel Taarabt's free-kick hit the arm of Jordan Henderson, before Daniel Agger headed in Liverpool's third.
Steven Gerrard's shot was cleared off QPR's goal-line as the Reds won easily.
Bottom-of-the-table QPR tamely went down to a 12th league defeat in 20 games this season and had the air of a side resigned to relegation, with eight points separating them from safety.
They had seen fellow bottom three sides Reading win and Southampton draw on Saturday and, while the least QPR might have showed is the stomach for a survival fight, they were missing that quality to an alarming scale.
Liverpool were quicker, hungrier and stronger and, although they were allowed the freedom to dominate the game, they did so with some delightful play which should help Rodgers feel better.
The livewire and menacing Suarez was again key to their win and he put his side 2-0 up in the first 16 minutes.
"Luis Suarez was electrifying for Liverpool in the first half. QPR improved belatedly but never really threatened. A massive improvement and miracle is needed if they are to avoid relegation. If they defend like they did in the opening half-hour then they will be in the Championship next year."
He jinked past a defender and had a 20-yard shot parried away, before giving his side the lead when he eased past centre-back Clint Hill and slotted a shot into the bottom corner.
The Uruguayan's second came when his low cross was cleared back to him by the sliding Nedum Onuoha to leave Suarez to side-foot in his 13th league goal of the season.
QPR playmaker Taarabt had a fair shout for a penalty when his free-kick hit the arm of Henderson, although referee Anthony Taylor was unmoved.
But QPR were crumbling against the endeavour and quality of the visitors and conceded a third when Agger headed in Gerrard's cross.
Soon after, Suarez shrugged off defenders Onuoha and Ryan Nelsen, before teeing up Gerrard - whose shot was cleared off the goal-line.
QPR fans booed their side off at half-time and their side continued to be outplayed after the break.
A Suarez shot was well saved by Julio Cesar, while Henderson shot high.
QPR midfielder Stephane Mbia curled a rare shot wide but the efforts came way too late.
The home side were 2-0 down with 13 minutes left against Liverpool last season before rescuing a 3-2 win which kick-started them beating the drop.
There was no such turnaround this time around, with Chelsea and Tottenham next up in the top flight for the Loftus Road club.
Liverpool assistant manager Colin Pascoe:
"That's probably the best we have played for a long time with the display in the first half. The way we took our chances was pleasing.
"Luis Suarez is superb. He's a maverick. He creates chances for himself, finishes them and is a great lad.
"It was great result from the lads and the way we performed in the first half secured the win. We were disappointed with the defeat by Stoke on Boxing Day and the response from the players was terrific."
Queens Park Rangers
- 33 Julio Cesar
- 03 Traore
- 06 Hill
- 15 Onuoha
- 17 Nelsen
- 02 Diakite (Granero - 63' )
- 10 Taarabt
- 11 Wright-Phillips (Fabio - 80' Booked )
- 40 M'bia Booked
- 09 Cisse (Derry - 46' )
- 12 Mackie
- 01 Green
- 05 Ferdinand
- 20 Fabio
- 04 Derry
- 14 Granero
- 32 Faurlin
- 23 Hoilett
- 25 Reina
- 02 Johnson
- 03 Jose Enrique (Suso - 71' )
- 05 Agger
- 37 Skrtel
- 08 Gerrard
- 14 Henderson (Lucas - 64' Booked )
- 19 Downing
- 24 Allen (Carragher - 87' )
- 31 Sterling
- 07 Suarez
- 42 Gulacsi
- 16 Coates
- 23 Carragher
- 21 Lucas
- 33 Shelvey
- 11 Assaidi
- 30 Suso
Live Text Commentary
Full Time The referee signals the end of the game.90:00 +1:32
Shaun Derry gives away a free kick for an unfair challenge on Steven Gerrard. Free kick taken by Leiva Lucas.90:00 +1:03
Stephane Mbia has an effort at goal from outside the box which goes wide left of the target.89:35
Free kick taken by Steven Gerrard.89:35 Booking
Booking Fabio Da Silva is booked.89:25
Free kick awarded for an unfair challenge on Raheem Sterling by Fabio Da Silva.87:44
Stewart Downing crosses the ball, Ryan Nelsen manages to make a clearance.86:25 Substitution
Substitution Joe Allen leaves the field to be replaced by Jamie Carragher.86:15
Centre by Adel Taarabt.84:47
Free kick awarded for an unfair challenge on Raheem Sterling by Fabio Da Silva. Free kick taken by Steven Gerrard.84:27
Foul by Ryan Nelsen on Luis Suarez, free kick awarded. Leiva Lucas restarts play with the free kick.82:03
Strike comes in from Stephane Mbia from the free kick, Jose Reina makes a comfortable save.82:03 Booking
Booking Leiva Lucas is booked.81:58
Leiva Lucas gives away a free kick for an unfair challenge on Adel Taarabt.81:28
Adel Taarabt fouled by Leiva Lucas, the ref awards a free kick. Adel Taarabt takes the direct free kick.79:37 Substitution
Substitution Shaun Wright-Phillips leaves the field to be replaced by Fabio Da Silva.79:28
The ball is crossed by Stewart Downing, blocked by Nedum Onuoha.78:08
Leiva Lucas gives away a free kick for an unfair challenge on Shaun Derry. Free kick taken by Esteban Granero.77:11
Stephane Mbia takes a shot. Save by Jose Reina.76:47
The ball is delivered by Jamie Mackie, clearance by Daniel Agger.
Free kick awarded for an unfair challenge on Adel Taarabt by Glen Johnson. Direct free kick taken by Adel Taarabt.75:01
The referee penalises Clint Hill for handball. Steven Gerrard delivers the ball from the free kick right-footed from right channel, save made by Soares Julio Cesar.73:57
Daniel Agger takes a shot. Nedum Onuoha gets a block in. Corner taken by Luis Suarez, save by Soares Julio Cesar.73:44
Short corner worked by Luis Suarez.72:21
The referee blows for offside. Jose Reina takes the free kick.71:32
Daniel Agger fouled by Jamie Mackie, the ref awards a free kick. Martin Skrtel restarts play with the free kick.70:33 Substitution
Substitution (Liverpool) makes a substitution, with Jesus Fernandez Saez coming on for Sanchez Jose Enrique.68:41
Stephane Mbia produces a right-footed shot from the edge of the box and misses to the right of the goal.65:57
Stephane Mbia takes a shot. Save by Jose Reina.65:14
Corner taken by Stewart Downing, Shaun Derry manages to make a clearance.62:21
Esteban Granero fires a strike on goal direct from the free kick.62:21 Substitution
Substitution Leiva Lucas comes on in place of Jordan Henderson.62:21 Substitution
Substitution (QPR) makes a substitution, with Esteban Granero coming on for Samba Diakite.62:21
Daniel Agger is adjudged to have handled the ball.60:42
Adel Taarabt takes a shot. Save made by Jose Reina.60:06
A cross is delivered by Armand Traore.58:51
Corner taken by Adel Taarabt.58:41
Samba Diakite takes a shot. Blocked by Daniel Agger.57:21
Unfair challenge on Daniel Agger by Jamie Mackie results in a free kick. Daniel Agger takes the direct free kick.56:38
Martin Skrtel restarts play with the free kick.56:38 Booking
Booking The referee cautions Stephane Mbia for unsporting behaviour.55:40
The official flags Jamie Mackie offside. Jose Reina takes the indirect free kick.53:32
Shot from deep inside the area by Jordan Henderson clears the bar.53:08
Corner taken short by Stewart Downing.52:45
Luis Suarez delivers the ball, Nedum Onuoha manages to make a clearance.50:18
Foul by Joe Allen on Adel Taarabt, free kick awarded. Direct free kick taken by Stephane Mbia.50:01
Corner taken right-footed by Steven Gerrard from the left by-line, save made by Soares Julio Cesar.49:43
Luis Suarez takes a shot. Soares Julio Cesar makes a brilliant save.47:12
Sanchez Jose Enrique fouled by Shaun Wright-Phillips, the ref awards a free kick. Luis Suarez crosses the ball in from the free kick, Adel Taarabt manages to make a clearance.45:01
The second half begins.45:01 Substitution
Substitution Shaun Derry joins the action as a substitute, replacing Djibril Cisse.45:00 +1:06 Half time
Half Time The whistle is blown to end the first half.44:33
Adel Taarabt has an effort at goal from outside the penalty area which goes wide right of the goal.41:57
The ball is swung over by Stewart Downing, clearance made by Nedum Onuoha.41:33
Foul by Samba Diakite on Steven Gerrard, free kick awarded. Jordan Henderson restarts play with the free kick.40:21
Shot by Steven Gerrard from outside the box goes over the net.39:21
Adel Taarabt takes a shot. Save by Jose Reina.39:03
The ball is swung over by Shaun Wright-Phillips, Glen Johnson makes a clearance.38:37
Glen Johnson gives away a free kick for an unfair challenge on Armand Traore. Free kick taken by Adel Taarabt.38:15
Djibril Cisse gives away a free kick for an unfair challenge on Daniel Agger. Free kick taken by Jose Reina.36:54
Steven Gerrard takes a shot. Armand Traore gets a block in.35:38
Raheem Sterling sends in a cross, save made by Soares Julio Cesar.34:14
Luis Suarez takes a shot. Ryan Nelsen gets a block in.31:44
Jordan Henderson has a shot on goal from outside the box which misses right.31:28
Raheem Sterling decides to take a short corner.31:23
The ball is delivered by Steven Gerrard, clearance by Shaun Wright-Phillips.30:26
Adel Taarabt takes a shot. Comfortable save by Jose Reina.29:44
Luis Suarez takes a shot. Blocked by Ryan Nelsen.29:10
Steven Gerrard takes the outswinging corner, Clint Hill manages to make a clearance.27:01
Assist by Steven Gerrard.27:01 Goal scored
Goal! - Daniel Agger - QPR 0 - 3 Liverpool Daniel Agger finds the back of the net with a headed goal from close in. QPR 0-3 Liverpool.26:49
Short corner taken by Stewart Downing from the right by-line.25:38
Steven Gerrard takes a shot. Save made by Soares Julio Cesar.25:11
Short corner taken by Stewart Downing.24:19
Stewart Downing takes a shot.21:35
Shot on goal by Luis Suarez from just inside the area clears the crossbar.21:02
Strike by Stephane Mbia from inside the six-yard box clear the bar.20:07
Free kick awarded for an unfair challenge on Stephane Mbia by Steven Gerrard. Strike on goal comes in from Adel Taarabt from the free kick.19:08
Djibril Cisse is ruled offside. Free kick taken by Martin Skrtel.17:15
Free kick awarded for a foul by Samba Diakite on Raheem Sterling. Free kick taken by Daniel Agger.16:32
Adel Taarabt takes a shot.15:23
The assist for the goal came from Stewart Downing.15:23 Goal scored
Goal! - Luis Suarez - QPR 0 - 2 Liverpool Goal scored by Luis Suarez from close range high into the middle of the goal. QPR 0-2 Liverpool.9:51
The assist for the goal came from Jordan Henderson.9:51 Goal scored
Goal! - Luis Suarez - QPR 0 - 1 Liverpool Luis Suarez fires in a goal from inside the area to the bottom left corner of the goal. QPR 0-1 Liverpool.3:20
Free kick awarded for a foul by Joe Allen on Adel Taarabt. Free kick taken by Stephane Mbia.2:51
Joe Allen takes a shot.2:36
Luis Suarez takes a shot. Soares Julio Cesar makes a save.1:44
Glen Johnson delivers the ball, Clint Hill manages to make a clearance.0:00
The referee gets the match started.
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