Two second half goals proved decisive as the Reds are now third in the Premiership behind Chelsea on goal difference.
However the outcome could have been so different had Sunderland striker Kenwyne Jones taken his early chance when one-on-one with Reds keeper Jose Reina.
David Ngog side footed home early in the first half giving the home side a timely boost.
The game was made safe when Martin Fulop failed to hold Ngog's cross and Yossi Benayoun was on hand to apply the finishing touch.
"I’m happy with the goal, but the most important thing is the points," Benayoun told Sky Sports 1.
"We were very disappointed. We expected to beat Middlesbrough — but we did a job tonight.
"It is important for everyone to show the supporters — even if it is not to win the league but to finish second and do our best."
Reds boss Rafa Benitez was pleased for the French teenager Ngog, who scored the first and created the second for Benayoun on his full home debut.
But Benitez said: "Ngog did a very good job; he scored an excellent goal, and that gave him confidence.
"Benayoun too was excellent, while we needed Jose Reina to make a very good save before we had scored.
"If they had scored early on when (Kenwyne) Jones got through, it could have been a lot more difficult.
"Generally we needed to keep calm, to find space and to be patient.
"Now it will be important to win our next league game at Manchester United; if we can do that things may well be a lot different at the top of the table."
Sunderland boss Ricky Sbragia also rued the early miss of Jones.
"Jones should have scored - and on any other day, he probably would have done so," he said.
"If we had scored then the game would have been very different. Liverpool would have become anxious and we would have given ourselves something to hang on to.
"Liverpool would have been under pressure. We did okay in the first half - but once they went ahead, it was always going to be difficult.
"We tried to change the system at that point by sending on Djibril Cisse, but the second goal soon after that really made it hard.
"Two down away to a team of Liverpool's quality is always going to be tough.
"We were also surprised by the way Liverpool played. We were expecting more long balls, but that is not what happened.
"We had to gamble by bringing on more strikers. But that gave them space - and once they scored the second, the game was going away from us."