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Luis Suarez scored a sublime double to pile the misery on relegation threatened Queens Park Rangers and end 2012 on a winning note for Liverpool at Loftus Road.
Suarez scored twice in the opening 16 minutes, first after turning past Clint Hill and secondly as he capitalised on Nedum Onuoha's half clearance.
Daniel Agger headed in his first ever Premier League away goal to make sure of the points, leaving QPR eight points from safety at the turn of the year.
Following wins for Wigan Athletic and Reading, QPR were under pressure to keep pace with their relegation rivals in the final Premier League game of 2012 against a Liverpool side who were without their unwell manager Brendan Rodgers.
But the absence of the Northern Irishman, who watched a limp performance in the defeat to Stoke City on Boxing Day, did nothing to stifle The Reds during the early stages in west London as Suarez tested the returning Julio Cesar early on after bamboozling Clint Hill, but the Brazilian beat away the early effort.
Cesar was however helpless to prevent his South American counterpart from handing the visitors the lead after 10 minutes, as Suarez again flummoxed Hill before he nestling the ball in the corner.
Liverpool's grip on the game tightened further still six minutes later as Suarez smashed home after Nedum Onuoha had intercepted his initial cross.
Adel Taarabt's tame free kick worked as only temporary respite for Rangers who after Ryan Nelson cleared from Glen Johnson's goalbound effort, and Cesar survived after dropping the ball at Henderson's feet, Agger headed in a third from Steven Gerrard's short corner.
Captain Gerrard would have made it four but for Armand Traore's goal line clearance as Liverpool looked to pile on misery on Harry Redknapp's side.
The half-time introduction of Shaun Derry added some steal to the QPR midfield in the second period and stemmed the flow temporarily before Henderson got free after more slack marking from a corner but blazed over from the edge of the area.
A spate of changes for both sides disrupted the flow of the second period, with Liverpool unable to add to their lead and The Hoops restricted to efforts from range, with Samba Diakite the main threat.
While the win lifts Liverpool above Rodgers' former club Swansea City into ninth and five points behind Merseyside rivals Everton, Rangers finish 2012 with one win this season and a seemingly desperate task of beating the drop from the Premier League for a second successive season.