Andriy Voronin struck to end Roy Keane's hopes of another dramatic Sunderland escape and finally gave Liverpool boss Rafael Benitez something to cheer about as the Ukrainian forward secured a 2-0 away victory.
Benitez had railed against what he perceived to be a catalogue of injustices against his side this week, but his mood will have lifted after Liverpool's solid display.
Mohamed Sissoko grabbed his first goal for the club in the 37th minute to put the visitors in control and Voronin sealed victory with four minutes to go.
In truth, Benitez's men were in control throughout and only some superb saves from Sunderland keeper Craig Gordon and the application of the home defence kept them at bay for so long.
If the team sheet was heavily weighted towards Liverpool in terms of quality, that determination Keane has instilled in his side kept them in with a chance up to Voronin's strike.
And one could not help recalling Michael Chopra's stunning injury-time winner on the opening day of the season against Tottenham, or the last-gasp equaliser at Birmingham four days later.
But it might have been very different if Voronin had properly capitalised on a dreadful error by home left-back Greg Halford with just 25 seconds on the clock.
Voronin pounced on Halford's short back pass and struck a low shot which squeezed under the impressive Gordon but wriggled agonisingly wide.
The early loss of Sami Hyypia with a bloody nose seemed set to matter little to Liverpool, who remained camped in the home half, while Sunderland suffered a bigger blow when Kieron Richardson limped off.
Xabi Alonso screwed a rising shot just wide in the 14th minute after Ryan Babel had cleverly laid off a Steve Finnan right-wing cross, but the expected succession of chances did not materialise.
Once again Paul McShane and Nyron Nosworthy held firm in the centre of the home defence, marshalled superbly by captain Dwight Yorke, and frustration slowly grew among the visitors.
That frustration should have increased in the 24th minute when substitute Anthony Stokes, on for Richardson, had a superb chance to give his side a shock lead.
Stokes was played clear by Chopra into the right side of the Liverpool box and hit his shot under the advancing Jose Reina, only for Agger to clear from the edge of the six-yard box.
Despite the visitors still failing to carve out too many clear-cut chances there was a feeling the home side had missed their opportunity and that was underlined in the 37th minute.
The lively Voronin laid the ball back to Sissoko on the edge of the box and the Mali international drilled a low right-foot shot past Gordon into the corner of the net.
With the visitors finishing the second half strongly, McShane needed a big interception to prevent Torres getting in a clear header, before Gordon grasped another effort by the Spaniard on the line.
The second goal seemed a matter of time early in the second half as Liverpool resumed their dominance and Xabi Alonso played in Torres, who was denied by the impressive Gordon.
Gordon saved Sunderland again three minutes later after Torres burst through the home defence and fired a fierce low shot that was brilliantly blocked by the £9million man.
If nothing else, Keane will have been pleased with his side's obvious desire not to accept defeat, and there was a growing suspicion that another late escape act might be on the cards.
Ross Wallace's deep cross into the Reds box in the 68th minute was punched away by Reina under pressure as the Stadium of Light crowd sensed a comeback.
But Liverpool's front line oozed class and Gordon was required again in the 79th minute to produce a point-blank save to deny Voronin in front of goal.
Finally Voronin extinguished those lingering Stadium of Light dreams with four minutes to go with a clinical finish to wrap up a productive afternoon for Benitez.