Christian Benteke was Liverpool's match-winner for the second time in five days as he plunged Sunderland deeper into relegation trouble.
The Belgium international, who scored the only goal against Leicester on St Stephen's Day, did it again at the Stadium of Light when he took advantage of some flat-footed defending 22 seconds into the second half to clinch a 1-0 victory.
That left the Reds level on 30 points with sixth-placed Manchester United, but the Black Cats seven points shy of safety at the halfway stage.
Liverpool might have won more comfortably had it not been for the first-half heroics of Sunderland goalkeeper Vito Mannone, who produced a string of fine saves including one breathtaking effort to deny Roberto Firmino in front of a crowd of 45,765.
Black Cats boss Sam Allardyce had vowed to get back to basics after seeing his side lose the last three games long before half-time with both Chelsea and Manchester City racing into 2-0 leads and Watford securing a 1-0 victory on Wearside with just four minutes gone.
In the circumstances, he will have been delighted to reach first the 20-minute mark and then the break all square at 0-0, although he was indebted to Mannone.
The home side got men behind the ball, allowing old boy Jordan Henderson, Emre Can and Philippe Coutinho to dominate possession in the middle of the field, and the visitors created several chances from which they might have taken the lead.
Mannone had to beat away Nathaniel Clyne's 30-yard piledriver with just five minutes gone and was then relieved to see Firmino miscontrol Coutinho's pass inside the penalty area after he had picked off Sebastian Coates' lose pass.
Coutinho then curled an effort just wide before landing a 17th-minute free-kick on the roof of the Italian's net as the Reds pushed for the opening goal.
But it was Firmino who almost broke the deadlock twice inside 11 minutes, first forcing Mannone to tip a long-range effort on to the post and then testing him once again with a firm header.
For their part, Sunderland created a series of half-chances with striker Jermain Defoe causing all kinds of problems for central defender Mamadou Sakho.
The former England striker called upon keeper Simon Mignolet to make a good eighth-minute save after spinning away from Sakho, and the Belgian was rooted to the spot as Fabio Borini curled a 33rd-minute shot just wide of his far post.
But all the good work was undone within 22 seconds of the restart when Adam Lallana managed to get a toe to Clyne's ball into the box and divert perfectly into the path of Benteke, who beat Mannone with ease to put his side ahead.
The home side responded in determined fashion and Borini thumped a 54th-minute shot into Mignolet's midriff after forcing his way into the box, and the Belgian had to make an important block from substitute Duncan Watmore's 78th-minute strike to cement the win.
However, substitute Jordon Ibe and Benteke both wasted glorious late opportunities to put the game to bed.
A happy Liverpool manager Jurgen Klopp said afterwards: "It's two goals, six points, that's the best thing for us. We go home now, we celebrate New Year, we come back and try to beat West Ham in the next game."
Meanwhile, it emerged last night that Sunderland boss Allardyce is closing in on his first January signing after French club Lorient accepted Sunderland's bid for 26-year-old defender Lamine Kone.
Lorient vice-president Alex Hayes said: "We have received an offer that we have accepted."