The Reds, who have scored 14 in their last three home matches, moved above Tottenham into fifth place having rarely been troubled by the Magpies.
Dirk Kuyt's eighth in his last seven league matches was sandwiched between another for Maxi Rodriguez, who hit a hat-trick in the 5-0 win over Birmingham last week, and one for the impressive Luis Suarez.
Only a goal for Andy Carroll, the subject of incessant abuse from the travelling fans, against his former club would have capped off the performance.
The £35million striker came on for the final 20 minutes but made little impact save for increasing the vitriol from the large away contingent.
Their anger at the way Carroll left them in January, with the club claiming he handed in a transfer request when made aware of Liverpool's interest, was understandable but he was never going to be a major player in this game having missed last week's victory with a knee injury.
The man who was the main reason Newcastle's record of just two wins at Anfield in their last 39 visits was not improved was Suarez.
Carroll's fellow deadline day signing has made a much greater impression and his inventiveness and workrate were a constant problem to the Magpies.
But it took even him a long while to get things going as, having played their best football of the season in demolishing Birmingham, the first half failed to reach anywhere near those heights despite taking a 10th-minute lead.
Raul Meireles had already bundled a shot wide from a cross by Glen Johnson, returning at left-back after a three-match absence with a hamstring injury, before the hosts went ahead.
Even then they required a slice of luck. Teenager John Flanagan's deep cross was only half headed clear by Mike Williamson and Rodriguez's follow-up volley took a big deflection off Danny Simpson.
It went downhill from there for Dalglish's side as they conceded too much territory to their opponents, who enjoyed a sustained period of possession without really threatening.
It was briefly broken by Jay Spearing's dipping shot, which Newcastle goalkeeper Tim Krul claimed at the second attempt with Meireles bearing down on him.
The home side were fortunate, however, that for all their time on the ball Newcastle struggled to carve out a decent opportunity.
Liverpool-born midfielder Joey Barton was the Magpies' main culprit as his delivery from set-pieces was poor.
The one time he did put a free-kick into a dangerous area Johnson headed behind for a corner, from which Kevin Nolan subsequently ballooned a shot over.
Liverpool's only other chance of the half saw Lucas Leiva's looping header easily caught by Krul, while Newcastle left-back Jose Enrique, a summer target for the Reds, had the final opportunity with a free-kick deflected behind off the wall.
For the second half Liverpool's full-backs switched sides, with Flanagan having been given a difficult time by Jonas Gutierrez.
But the youngster was almost caught napping within seconds of the restart as Nolan's low cross was side-footed wide by Barton at the far post.
Luck was certainly on Liverpool's side as Suarez almost scored with a deflected shot which hit the side netting and Rodriguez hit the crossbar as he tried to centre from the left.
There was a hint of fortune about Liverpool's 59th-minute second when Suarez isolated Williamson wide on the left from Jose Reina's kick and was sent tumbling by the defender right on the edge of the penalty area close to the byline.
Referee Peter Walton, who had frustrated the home crowd with a number of decisions, had no hesitation in pointing to the spot to allow Kuyt to score.
The Holland international should have doubled his tally with a free header seven yards out minutes later but missed the target.
Suarez made no such mistake in the 65th minute when he exchanged passes with Kuyt to sidefoot under Krul from 10 yards.
With the game safe Dalglish sent on Carroll for Rodriguez with 20 minutes to go, just before Meireles' diving header was deflected behind by Fabricio Coloccini.
Carroll barely touched the ball as his side ran out comfortable winners and, despite having played one match more than Tottenham, Liverpool are strong contenders to take the Europa League berth.