Kenny Dalglish secured his first win after returning to the helm after Liverpool beat Wolverhampton Wanderers 3-0 at Molineux on Saturday lunchtime.
Fernando Torres broke the deadlock in a scrappy contest on 36 minutes after generously being setup by Raul Meireles for the simplest of tap ins.
The Portuguese ace did get on the score sheet shortly after half-time, however, with a sure-fire goal-of-the-season contender as he expertly smashed a 25-yard volley into the top corner.
Wolves pressed in an attempt to reduce the arrears late on, but Torres struck again at the death to help the Reds claim an important three points.
Buoyed by a much-improved attacking performance during last weekend's 2-2 draw with Everton at Anfield, Liverpool journeyed to Molineux aiming to secure not only the first win of Kenny Dalglish's second coming, but also their second on the road in the Barclays Premier League in 2010-11.
Indeed, the manager's satisfaction at his side's derby display was reflected in his team selection with just one change made - Christian Poulsen replacing Jay Spearing in midfield.
However, despite their lowly position of 19th in the table, Wolves demonstrated they are anything but pushovers by winning 1-0 at Anfield in late December, while they could also consider themselves highly unfortunate not to have taken something from a recent narrow defeat against Manchester City at Eastlands.
In fact, the Reds' last win at Molineux was way back in April 1979, while they'd managed just two clean sheets in their last nine trips to the Black Country.
But the visitors fashioned the first chance on a chilly Midlands afternoon when only a block by Christophe Berra prevented Poulsen giving them an eight-minute lead after good interplay between Glen Johnson and Lucas Leiva carved open a chance for the Dane.
Wolves then had goalkeeper Wayne Hennessey to thank for thwarting Torres on 21 minutes. Meireles's inch-perfect pass sent the Spaniard bearing down on goal, only to see his effort beaten away after deftly stepping inside the challenge of Richard Stearman.
Nevertheless, it was proving a real midfield scrap with neither side able to stamp their authority on a bitty contest.
Liverpool were looking the more dangerous, though, and after Meireles had Hennessy scrambling across his line courtesy of a 31st minute volley that narrowly evaded the target, the Wolves stopper needed to be alert to block Maxi's attempt from eight yards.
The breakthrough duly arrived on 36 minutes. Poulsen pierced open the Wolves backline with a through ball that sent Meireles surging beyond and into the area. Faced with Hennessey, the Portuguese midfielder looked up and selflessly squared for Torres to tap into an unguarded net.
The Reds were good value for their half-time lead, though only a stoppage-time save by Pepe Reina kept their advantage intact after Stephen Hunt's free-kick had deflected dangerously into the path of Nenad Milijas inside the six-yard box.
A sloppy spell in the immediate aftermath of the break had ultimately prevented Liverpool from collecting all three points against Everton last time out.
But it wasn't to be a case of history repeating itself at Molineux and after Hennessey had denied Kuyt, Meireles doubled the Reds' lead on 50 minutes with a goal of sublime quality.
Daniel Agger's long free-kick forward was cleared away from the edge of the box by the head of Berra but fell to the visitors' No.4, who, in the blink of an eye, dispatched a technically flawless full volley into the top corner from fully 25 yards.
The goal stirred Wolves, with Steven Fletcher forcing a stop out of Reina with a stinging drive from the edge of the box while Meireles again tested Hennessey at the other end.
Jonjo Shelvey spurned the chance of a first Liverpool goal with just over 15 minutes remaining when he stabbed wide after a fine counter-attacking move involving Torres and Meireles.
The home side enjoyed some concerted pressure in the dying stages, but they were unable to trouble Reina.
And Liverpool furthered their lead in stoppage-time when a fine spell of possession resulted in Kuyt setting up Torres for a simple finish to ensure Dalglish claimed the first win of his second Anfield tenure.
Liverpoolfc.tv man of the match: Raul Meireles