Manchester City's comprehensive victory over champions United in Tuesday's derby meant that all eyes were on Anfield as Brendan Rodgers' side attempted to respond.
Sitting a point behind City - who now have two games in hand - and four adrift of Chelsea, it was essential that Liverpool grabbed a seventh successive league win to stay in touch.
After an opening 30 minutes of few chances, captain Steven Gerrard was on hand to settle the palpable nerves with a stunning free-kick that Vito Mannone could not keep out.
With order restored, Liverpool appeared on course for a comfortable night when Daniel Sturridge grabbed a 20th league goal of the campaign - in the process ensuring that he and Luis Suarez became the first Liverpool duo since Roger Hunt and Ian St John in 1963-64 to pass the mark in one season.
However, Sunderland threatened a twist in the tale when the impressive Ki Sung-Yueng pulled one back with 14 minutes left.
The visitors continued to press forward thereafter but fell short of a leveller that would have taken them to within two points of safety.
The home side looked every bit like a team who had not suffered defeat in 11 league games as they bossed the opening exchanges.
Yet, for all their attacking verve, Liverpool struggled to fashion clear-cut opening as Sunderland showed great restraint by largely operating with 10 men behind the ball.
Such discipline was severely lacking as the hosts took the lead six minutes before half-time, however.
Philippe Coutinho took advantage of Lee Cattermole's heavy touch to nip in and free Suarez, who was clumsily brought down on the edge of the area by Santiago Vergini.
The Argentinian was perhaps fortunate to escape with just a yellow card, although that was scant consolation when Gerrard's subsequent curler proved too powerful for Mannone – who did not help himself with a step to his right just before Gerrard struck the free-kick into the opposite corner.
To their credit, Sunderland almost found an immediate response as Connor Wickham - only recalled from a loan spell at Leeds this week - saw a deflected effort force a good save from former Sunderland goalkeeper Simon Mignolet.
Any hopes of a turnaround were virtually extinguished immediately after the break as Sturridge cut inside Andrea Dossena before seeing his curling effort deflect off Wes Brown and beyond a helpless Mannone.
Buoyed by grabbing his 20th Premier League goal of the campaign, Sturridge almost added another soon afterwards - only to see his effort hit Suarez.
The game had suddenly taken on and end-to-end nature, with Cattermole and Sturridge rattling the crossbar in quick succession.
Sunderland set up a tense finale as Ki, who impressed having come off the bench, headed home fellow substitute Adam Johnson's corner.
But despite their late efforts, the visitors could not fashion a second, as Liverpool held on to three vital points.
