Liverpool moved to within four points of fourth-placed Manchester City after a goal in each half from Raheem Sterling and Joe Allen gave Brendan Rodgers’ side a 2-0 victory over Newcastle United at Anfield.

Only a week ago Liverpool’s hopes of making it back to the promised land of the Champions League appeared to have been dashed by a 4-1 drubbing at the hands of Arsenal. But the continued slump of last season’s champions has given Liverpool an opening that they appeared in no mood to decline on Monday.

Sterling, who continues to be the source of much speculation over his unsigned contract, gave a robust case for why he should get anything he asks for with a sublime piece of skill and fine curling finish to give the hosts the lead just nine minutes in. At that point it appeared that, a week on from their derby defeat to Sunderland, it could be another chastening 90 minutes for a Newcastle side that continues to drift aimlessly toward the end of a lost season.

Rodgers kept with the 4-3-3 formation he brought back for the FA Cup quarterfinal replay victory over Blackburn Rovers in midweek, but, with Daniel Sturridge again out through injury, Philippe Coutinho was deployed in an unfamiliar false-nine role. In the early going the Brazilian was superb as the hub of a Liverpool team whose intensity tore through an insipid Newcastle side. But Liverpool tailed off, with complacency perhaps creeping in, and Newcaslte could and perhaps should have got back into the contest. Manager John Carver will still be raging about an incomprehensible decision not to award a penalty when Ayoze Perez went down under Dejan Lovren’s wild challenge.

And with 20 minutes remaining the points were effectively sealed when Allen struck home at the second attempt after just one of the many incidents of hapless Newcastle defending. All that was left was for the visitors’ miserable evening to be complete when Moussa Sissoko was shown a second yellow card for an ugly challenge on Lucas Leiva that, in truth, should have seen him receive a straight red.

It was a drama-free climax, and, although Liverpool should have won even more convincingly, Rodgers’ tactical shakeup looks to have again been vindicated. His switch to three at the back bought a 13-game run without defeat to revive their top-four hopes, and now, after, that system was found wanting in defeats to Manchester United and Arsenal, there are signs his latest alteration could do similar.

The decision to start with Coutinho as a deep-lying striker supported by the pace of Sterling and the fit again Jordan Ibe certainly paid off in the early going. The first goal was a case in point. Coutinho laid the ball off, Jordan Henderson swung it to the left of the box for Sterling and the 20-year-old brilliantly did the rest with some delightful footwork.

Newcastle, dropping deep and applying no pressure, had no answer for Coutinho’s movement and the verve with which Liverpool streamed forward. The only thing preventing Liverpool from being out of sight in the first 30 minutes was too often the lack of the right final ball.

But Liverpool couldn’t maintain their blistering early tempo and with that slowing down came some sloppiness along with signs that the defense remains a considerable concern. Lovren got it badly wrong when he swiped for the ball in his own box and clattered the leg of Perez. The Croatian was mighty fortunate that referee Lee Mason was surely one of the few people inside Anfield who didn’t see it as a penalty. Newcastle were denied again before the break, with Simon Mignolet doing well to keep out a Perez header.

Still, it seemed only a matter of time before Liverpool struck again. Sterling should have provided the second goal 11 minutes into the second half, but somehow, after a woeful botched clearance from Ryan Taylor, he shot wide of the post form six yards. Continuing a mixed evening for the man in the spotlight, Sterling missed another presentable opportunity when volleying over from similar distance late on.

But by that point Liverpool had already got the second goal they required to ensure victory. It came after a half-cleared corner was helped back into the danger zone and Mike Williamson failed to clear allowing Allen to lash the ball home.