The Posh were never in the frame against a rampant Newcastle who could have quite easily have doubled their winning margin against mediocre opposition.
A first United goal from Jonas Gutierrez followed by an Andy Carroll header effectively killed off the game as a contest after just 18 minutes.
Danny Simpson's first goal in a black and white shirt opened up a 3-0 advantage early in the second half, before Dean Keates pulled back a late consolation.
Demonstrations took place about an hour before the start of the match outside of the main entrance.
Disillusioned Newcastle fans vented their anger at owner Mike Ashley following the announcement earlier in the week that he had changed the ground's name to sportsdirect.com at St James' Park.
Once the match started the fans continued to show their displeasure towards the owner with chants of 'we want Ashley out' and stewards made supporters remove a banner which said exactly the same and later ejected some fans.
On the park, Newcastle dominated from the off with fast, flowing football and Posh had no answer.
The big surprise was that it took 15 minutes for United to score, but it was worth the wait as Gutierrez finally got off the mark for the club.
The Argentine broke from the left from the halfway line and tricked his way by four defenders before rifling his shot beyond Joe Lewis.
Bu there was no celebrations from Gutierrez and the reason why was pinpointed four minutes later when he limped off to be replaced by Ryan Taylor.
By then United had opened a commanding 2-0 lead, Carroll rising head and shoulders above the Posh defence to head in a Danny Guthrie corner.
And it was almost three after 28 minutes, Guthrie cleverly losing his marker on the edge of the box only to see his cross shot cannon to safety off the upright.
This was only the third ever league encounter between these two sides, United having completed the double in the Championship title winning 1992-93 season.
And with a third defeat looking on the cards after an embarrassingly one-sided first half, Posh boss Darren Ferguson made a double switch at the break with Aaron McLean and Paul Coutts replacing Danny Rose and Toumani Diagouraga respectively.
But hopes of a fight back were quashed after 52 minutes with yet another first goal for the club, this time from Simpson.
Another flowing move tore Posh apart with Marlon Harewood picking out Simpson on the right, whose delivery caught out everyone including keeper Lewis and sailed into the net.
Peterborough finally managed a shot on target after 56 minutes through Chris Whelpdale which was saved by Steve Harper, who then held on to a McLean drive.
At the other end Lewis foiled Kevin Nolan with an acrobatic save at the expense of a corner from which Harewood had a header cleared off the line.
Throwing caution to the wind, Posh upped the ante and posed problems forced superb saves from Harper to deny George Boyd and Keates.
It was second time lucky for Keates after 80 minutes when the broke invitingly inside the box and this time he made no mistake to reduce the arrears to 3-1.