Liverpool can rarely have found three points so easy to obtain on their travels and, but for some woeful Fernando Torres finishing, the boys from Anfield could easily have netted six or seven.
Had Torres put away even half of his opportunities he could have finished up with a hat-trick.
With Steven Gerrard inspirational in opening the scoring and having a hand in the other two, Liverpool ran the show at a canter and made a mockery of Newcastle.
And to make it even more frustrating for Allardyce, the home fans vociferously questioned ever decision the manager made.
While Liverpool glowed, Newcastle were inept, outplayed, outfought and outclassed in every department, and make no mistake about, the obvious lack of confidence throughout the side leaves Allardyce with a major problem.
James Milner, Joey Barton and keeper Steve Harper were all relegated to the bench after starting in the 1-1 draw last time out at Sunderland.
Shay Given returned from injury, skipper Geremi was recalled as was Obafemi Martins, who came in for injury victim Michael Owen.
Rafael Benitez did his usual tinkering, but could not find a place for Peter Crouch who scored twice in five days last week for England in Austria and then at Wembley against Croatia.
Crouch had to settle for a place on a strong looking Liverpool bench.
Liverpool looked like creating a chance every time they ventured forward and the biggest surprise was that it took until the 28th minute for them to go ahead with a stunning Gerrard free-kick.
Some 30 yards from goal, Lucas Leiva rolled the ball to the right and Gerrard's drive flashed into the top corner beyond Given.
The frustrated home fans had to wait until the 38th minute for a chance of any sorts that saw Alan Smith control and volley across the face of the Liverpool goal.
Jeered off the pitch at half-time, it could have been much worse.
A misplaced Charles N'Zogbia pass was whipped forward for Torres. Given dubiously blocked the ball with his chest but United's defenders continued to get in the way of each other and Torres was left with an open goal only to see his shot strike the foot of the post and bounce clear.
Many of the fans had not even returned to their seats when Dirk Kuyt put Liverpool two up.
Gerrard's corner was flicked on by Sami Hyypia and Kuyt knew little about it as the ball hit his knee and ended up in the net.
Newcastle fell 3-0 behind with a stunning move and finish when Ryan Babel finished off a 17-pass move after 66 minutes.
On for Harry Kewell, Babel finished off by working a one-two with Gerrard and Given was once again beaten.
Hundreds of fans poured from the ground as others taunted Allardyce with chants of 'You don't know what you're doing' and 'We've only had one shot' before booing the team off the pitch.