QPR's survival hopes were dealt a major blow as Luis Suarez inspired Liverpool to a comprehensive 3-0 victory despite the absence of manager Brendan Rodgers.
Liverpool dominated from the outset and coasted to victory even without Rodgers, who was unwell and too sick to be on the touchline.
Suarez got the visitors off to a flyer with two goals inside the opening 16 minutes before Daniel Agger nodded the them further ahead in the 28th minute. Despite an improved second-half performance from the hosts, Liverpool were never in any real danger of losing grip of proceedings.
The defeat leaves QPR bottom and eight points adrift of safety heading into a tough January, which starts with a trip to rivals Chelsea.
The west Londoners started poorly, with returning goalkeeper Julio Cesar tested inside three minutes. Suarez jinked past Clint Hill and unleashed a fierce strike that the Brazilian, recalled in place of Robert Green, could only parry.
Cesar may have wished he had stayed on the bench given the pressure he was under from the outset, with Suarez netting his first of the afternoon in the 10th minute. The Uruguayan collected a pass from Jordan Henderson and ghosted past Hill with worrying ease, before striking low past the goalkeeper.
It was the 14th time this season that QPR had conceded the opening goal and in the 16th minute Liverpool doubled their advantage. Suarez was again both scorer and creator, bursting along the byline from the right to produce a cross that Nedum Onuoha could only block straight into the striker's path, allowing him to net again.
Liverpool did not have to wait long for their third goal, as Steven Gerrard collected a short corner and sent in a right-wing cross for Agger to nod home.
Jordan Henderson was inches away from Liverpool's fourth with a drilled 20-yard strike, before a Gerrard effort was cleared off the line by a combination of Armand Traore and Nelsen.
The Hoops emerged for the second half with Shaun Derry on in place of Cisse as Redknapp switched to a 3-5-2 formation. The move to make the home side sturdier worked for the most part, but the Reds remained a threat and they were able to see the game out comfortably.