Super Suarez proves his worth to purring Dalglish

Liverpool 1 Queens Park Rangers 0: Liverpool's Uruguayan striker answers critics with match-winning display

You cannot keep a good man down – not even one with a bit of devil in him. Five days after creating a fresh controversy by earning an FA misconduct charge for an alleged hand gesture at Fulham fans, Luis Suarez stole the headlines for the right reasons yesterday with an outstanding display in this narrow, but richly deserved Liverpool victory.

Suarez scored the only goal after 47 minutes, heading a Charlie Adam cross past Radek Cerny, but would have been the game's dominant figure even without his decisive strike that secured Liverpool a first home success since September and lifted them into sixth place, above Newcastle on goal difference.

Kenny Dalglish had showed reporters on Thursday a DVD package designed to persuade them that the Uruguayan is less sinner than sinned against; here was evidence of a less disputed fact, namely Suarez's ability to illuminate a football field with his presence. A delighted Dalgish said afterwards: "It will be nice headlines tomorrow for him. He scored with a header which doesn't happen too often and played really well."

The Uruguayan, who had not scored in the Premier League since 1 October, was a menace to the QPR defence with not just his ability and inventiveness but also, during a first half of missed opportunities, for his sheer irrepressibility. Liverpool had surrendered an 11-match unbeaten run at Fulham on Monday and began intent on making amends, setting the tone for a display that produced 15 shots on target with three corners inside the first three minutes.

Suarez was at the heart of it and might have had a hat-trick inside the first 15 minutes. After nodding a Stewart Downing cross straight at Radek Cerny, Suarez played a cute one-two with Maxi Rodriguez, a lively accomplice, only to screw his shot wide. Suarez had begun the day as owner of an unwanted Premier League statistic for most shots off target (26) and he added another, flashing a shot from a tight angle that flew between Cerny and the near post but right across the goalline.

Suarez was not the only profligate one – on the half-hour Dirk Kuyt sent Maxi running clear but Cerny got a hand to his sidefooted finish – but before long he was at it again, failing with an attempted lob of the goalkeeper, then lashing the rebound wide.

Rangers have won more games away from Loftus Road than at home but Liverpool's passing and moving had them chasing shadows. "Some of the football we played in the first half was brilliant," purred Dalglish. Still, there remained the question whether they could press home their advantage. The home crowd, mindful of damaging draws here with the other promoted sides, Norwich and Swansea, remained subdued until Suarez – who else? – caused Anfield to explode into noise moments after the restart.

Adam was the instigator, stepping away from Shaun Wright-Phillips on the right flank and crossing into the six-yard box where Luke Young had left Suarez free to bury his header past Cerny.

QPR lost Anton Ferdinand with a hamstring injury and they might have lost more goals too but for the excellence of Cerny, the visitors' third-choice keeper.

The Czech stretched out a long arm to touch a Maxi shot on to the post. Maxi was foiled again by Cerny after breaking free after a pinball exchange with Suarez. "Radek Cerny was fantastic," said Neil Warnock, the visiting manager. "I am really pleased for him. He is a top professional and at 37 never thought he'd play another game in the Premier League."

The ghosts of Liverpool's five previous home draws ensured some late jitters with Danny Gabbidon spurning an opportunity to equalise after 72 minutes, when he turned over from the edge of the six-yard box. That was one of several anxious moments from high balls into the home box.

Liverpool (4-2-3-1): Reina; Johnson, Skrtel, Agger, Enrique; Henderson, Adam; Downing (Shelvey 86), Kuyt, Maxi (Bellamy 78); Suarez.

QPR (4-4-2): Cerny; Young, Ferdinand (Orr 50), Gabbidon, Traore; Wright-Phillips, Barton, Faurlin, Smith (Campbell 66); Mackie (Hill 78), Bothroyd.

Referee: Lee Mason

Man of the match: Suarez (Liverpool)