Liverpool captain Steven Gerrard hails Luis Suarez and 'best performance of the season'.
QPR 0 Liverpool 3
The Anfield club scored three goals in 18 minutes, with Luis Suarez getting two and Daniel Agger the other, and were in control beyond that.
They were hardly tested by a Rangers side in big trouble at the bottom and Gerrard, the Liverpool captain, said his men had been on the money.
"I wouldn't say it was easy, that would be disrespectful to QPR, they are having a tough time," he told Sky Sports 1. "If we started well we knew we could quieten the crowd and that was the best we've played this season in the first half.
"The plan was for us to get more goals, but Harry Redknapp is a top manager and QPR changed things in the second half, so credit to them."
Suarez's goals added further to the exceptional season he has had and Gerrard said of the Uruguayan: "He's been brilliant ever since he came here. He's a magician.
"These clubs have to play him twice a season but we have to play against him every day!"
Liverpool dominated from the outset and coasted to victory even without their manager Brendan Rodgers, who was too unwell to be on the touchline.
The defeat leaves QPR bottom and eight points adrift of safety heading into a tough January, which starts with a trip to Chelsea.
The West Londoners started poorly yesterday, with the 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 in the 10th minute.
The Uruguayan collected a pass from Jordan Henderson and ghosted past Hill 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 goal line from the right to produce a cross that Nedum Onuoha could only block into the striker's path, allowing him to net again.
Adel Taarabt and Djibril Cisse tried and failed with audacious efforts in a bid to reduce the deficit, although Liverpool were still in the ascendancy.
And they did not have to wait long for their third goal, as Gerrard collected a short corner and sent in a right-wing cross for Agger to head home in the 28th minute.