An outrageous strike from Xabi Alonso and Dirk Kuyt's first goal for Liverpool saw off Newcastle.
Xabi Alonso is congratulated after his spectacular strike
Kuyt ended Liverpool's five-hour goal drought when he slid in to convert Steve Finnan's cross after Alonso's exquisite pass had created the chance.
And after the break, Alonso produced another moment of brilliance when he shot from inside his own half to leave the slipping Steve Harper groping air.
Luis Garcia had earlier hit the post as Liverpool dominated poor opposition.
However, had Newcastle carried any threat at all, Liverpool may have been punished for their profligate finishing.
Craig Bellamy should have scored when through in on goal but dinked his effort wide, while Garcia shot straight at Harper early on.
As for Newcastle, they had two penalty appeals waved away as they vainly tried to make an impact.
Both involved Shola Ameobi - and neither looked that convincing as first the striker tangled with Danny Agger and then claimed handball off Jamie Carragher.
And aside from a couple of long-range efforts, that was about all a blunt Newcastle attack could muster.
Yet Liverpool almost failed to take advantage and at times looked every inch a side with a confidence crisis in front of goal.
They had come into the game desperate for a goal after more than 300 minutes without one.
Kuyt, despite looking lively throughout and notching his first goal since joining Liverpool from Feyenoord, was also guilty of sloppy finishing.
He guided a shot wide after Garcia had pulled back well from the by-line and also directed a header off target when he should have been celebrating a hat-trick.
The chances kept coming for Liverpool - particularly after the interval - but Fabio Aurelio's free-kick was well saved and Steven Gerrard fared similarly with his set-piece effort.
And it took a moment of exceptional skill for Liverpool to add to Kuyt's opening strike.
Looking up, and still well in his own half, Alonso spotted Harper off his line and launched an arrow of a shot over the keeper and into the corner of the net.
The Spaniard scored against Luton in the FA Cup last season - his last goal - from a similar distance, but it pales hugely in comparison.
It will not be a memory, though, that Harper will cherish when the replays are shown over and over again.
To some extent, Alonso's goal put gloss on a Liverpool performance that lacked cutting edge.
But it was a victory that was deserved, while Newcastle will need to improve - and quickly.
Liverpool boss Rafael Benitez:
"I was waiting for Alonso to pass and I would have spoken to him about it, but after he scored I said to him 'good, fantastic goal'.
"Not only did we score two goals but we created a lot of very clear chances.
"we have confidence in ourselves and we can improve. We could have scored three or four goals and deserved to win."
Newcastle manager Glenn Roeder:
"I feel let down by Mark Halsey.
"I have had a chat with Mark and even Rafa Benitez believes it was a penalty.
"He moves his hand sufficiently to block Shola's shot and that was the turning point."
Liverpool: Reina, Finnan, Carragher, Agger, Aurelio, Luis Garcia, Alonso, Sissoko, Gerrard (Gonzalez 85), Bellamy, Kuyt (Crouch 82).
Subs Not Used: Dudek, Hyypia, Warnock.
Booked: Luis Garcia.
Goals: Kuyt 29, Alonso 79.
Newcastle: Harper, Carr, Ramage, Moore, Babayaro, Milner (N'Zogbia 68), Parker, Emre, Duff, Martins (Rossi 76), Ameobi (Sibierski 82).
Subs Not Used: Krul, Butt.
Ref: M Halsey (Lancashire).