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 Boxing 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.
TWEET OF THE MATCH
"Sam chewing away during the one minute silence at Sunderland v Liverpool. Is he sponsored by Wrigleys" - Maybe he is just trying to emulate his friend Sir Alex Ferguson, Sir Alan Sugar (@Lord_Sugar).
Vito Mannone: 8
Billy Jones: 6
Sebastian Coates (Yedlin, 72 mins): 5
Wes Brown: 6
Patrick van Aanholt: 6
Yann M'Vila: 7
Lee Cattermole (Capt): 7
Jack Rodwell (Watmore, 30 mins): 6
Adam Johnson (Lens, 63 mins): 5
Jermain Defoe: 7
Fabio Borini: 7
Duncan Watmore: 6
Jeremain Lens: 5
DeAndre Yedlin: 6
Simon Mignolet: 7
Nathaniel Clyne: 7
Dejan Lovren: 6
Mamadou Sakho: 5
Alberto Moreno: 6
Adam Lallana: 6
Jordan Henderson (Capt) (Lucas, 61 mins): 7
Emre Can: 8
Philippe Coutinho (Ibe, 83 mins): 7
Roberto Firmino (Toure, 90+3 mins): 7
Christian Benteke: 6
Lucas Leiva: 6
Jordon Ibe: 5
Kolo Toure: 6
Emre Can was at the centre of Liverpool's best work, accepting the ball deep and linking with Jordan Henderson and Philippe Coutinho to feed the men ahead of them.
MOMENT OF THE MATCH
Sunderland keeper Vito Mannone's superb fingertip save from Roberto Firmino to turn the ball on to the post.
VIEW FROM THE BENCH
Sunderland boss Sam Allardyce will have been pleased at his side's first-half resilience, but hugely disappointed with their failure to switch back on after the break, which ultimately proved fatal. Liverpool counterpart Jurgen Klopp will have been impressed with his team's patience on a night when they had plenty of the ball, but were repeatedly thwarted by Mannone.
MOAN OF THE MATCH
Referee Kevin Friend quite literally got involved in the game on two occasions, blocking attempted passes, one in the midst of a dangerous-looking Sunderland break.
WHO'S UP NEXT
West Ham v Liverpool (Barclays Premier League, Saturday January 2)
Sunderland v Aston Villa (Barclays Premier League, Saturday January 2)
Liverpool boss Jurgen Klopp was delighted his team found a way to win against a Sunderland side that he did not feel were easy to play against.
"We were the better team and you could see that the pressure on both teams was big," he told Sky Sports 1. "A little bit more for Sunderland because of the intensity of the last weeks and months.
"You could help yourself if you got an early goal, we didn't but we did not do too bad in situations against a very good defending team. They were only defending so that makes it pretty hard for us because you don't get space and you always have to go again and slow down the game.
"Then we made the goal after half-time and we controlled something like the game.
"They were waiting for set-plays, they are difficult to defend but we did it. We could have got made a second or third one, we didn't, we had to wait until the final whistle."
Allardyce felt the Black Cats were unfortunate in the manner that Liverpool got their goal but praised his side's effort, although he conceded a lack of killer instinct in the final third.
"We didn't really produce enough quality," he said. "When we did we got good chances, we couldn't finish them off but we could have done more with the opportunities in terms of our final third quality - we need to try and get that a little better.
"A resilient performance, one where Liverpool never really looked like creating too many clear-cut chances or opportunities and if we can build on that scenario and get a bit more luck then we'll try to go up the other end, get a result and score a goal.
"The injuries are a problem. We're facing another centre-half who's come off injured so we'll have to wait and see how Seb (Coates) is.
"I thought Wes (Brown) did great today. I thought the team did well overall, a good shape to the side. They're playing a Liverpool side that's got a huge amount of money spent on it and often matched them."