Luis Suarez scored the only goal against QPR as a dominant Liverpool avoided a fifth successive home draw and climbed to sixth in the table.
QPR kept the hosts out until 69 seconds into the second half when an unmarked Suarez headed in Charlie Adam's cross.
It was Suarez's first league goal since netting against Everton on 1 October - and comes in the week he was charged by the Football Association for a hand gesture made towards Fulham fans.
Radek Cerny made several superb saves.
But his team rarely threatened, except from corners, and almost conceded an own goal when Shaun Wright-Phillips hit the bar late on.
Uruguayan Suarez, 24, had scored five goals for his country since his last Premier League strike.
But he has consistently been in the headlines as he faces a second FA charge relating to an alleged racial slur against Manchester United defender Patrice Evra.
If the win kept Liverpool on the fringes of the race for the Champions League places, it also left nagging doubts about their stuttering home form, which has seen them draw with both title-chasing Manchester clubs but also Sunderland and the two sides promoted with QPR - Norwich and Swansea.
The game, and particularly the opening 45 minutes, gave a taster of why Kenny Dalglish's side have drawn so often this season and failed to secure more points at Anfield.
Liverpool dominated possession, won 10 corners, and created a reasonable number of chances - but rarely forced Cerny into serious action.
/football on Youtube brings you the latest football news, transfer rumours and footballing gossip from the English Premier League and European Champions League.
QPR kept the hosts out until 69 seconds into the second half when an unmarked Suarez headed in Charlie Adam's cross.
It was Suarez's first league goal since netting against Everton on 1 October - and comes in the week he was charged by the Football Association for a hand gesture made towards Fulham fans.
Radek Cerny made several superb saves.
But his team rarely threatened, except from corners, and almost conceded an own goal when Shaun Wright-Phillips hit the bar late on.
Uruguayan Suarez, 24, had scored five goals for his country since his last Premier League strike.
But he has consistently been in the headlines as he faces a second FA charge relating to an alleged racial slur against Manchester United defender Patrice Evra.
If the win kept Liverpool on the fringes of the race for the Champions League places, it also left nagging doubts about their stuttering home form, which has seen them draw with both title-chasing Manchester clubs but also Sunderland and the two sides promoted with QPR - Norwich and Swansea.
The game, and particularly the opening 45 minutes, gave a taster of why Kenny Dalglish's side have drawn so often this season and failed to secure more points at Anfield.
Liverpool dominated possession, won 10 corners, and created a reasonable number of chances - but rarely forced Cerny into serious action.
/football on Youtube brings you the latest football news, transfer rumours and footballing gossip from the English Premier League and European Champions League.
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