An own goal Garry Flitcroft sent the Magpies into an early lead and they never looked back.
Alan Shearer, dropped from the last starting line-up by Sir Bobby Robson, added a second after 16 minutes and Andy O'Brien scored late in the game to round off a convincing performance.
The score would probably have been greater had referee Dermot Gallagher not waved away two strong penalty appeals.
In the third minute United had a shout turned down when Dominic Matteo brought down Lee Bowyer on the turn in the visiting box, having been played in by from Craig Bellamy.
Five minutes later Laurent Robert swung in the Magpies' first corner of the game and the recalled Flitcroft, out of favour under the departed Souness, inadvertently poked the ball past Brad Friedel to send United into the lead.
Robert then drove a fierce 30-yard free-kick inches wide before Gallagher, who had already angered St James' with his earlier decision, further enraged the Toon Army by turning down another blatant penalty.
Bowyer was again felled, this time by Morten Gamst Pedersen, as he arrived late in the box to get on the end of an inviting ball.
Undeterred, Newcastle pressed on and doubled their lead. Aaron Hughes sent Bellamy away on the left and the Wales striker's cross was met by Shearer at the far post, with Friedel unable to beat it out.
United began to look more like the team Robson had led to third in the Premiership two seasons ago, rather than the shambles beaten at Villa Park two weeks ago.
The game lulled after Newcastle's second, but one-time United target Brett Emerton almost snapped both teams out of their lethargy with a shot from nothing in the 35th minute, with his long-range effort dipping just too late.
Before the half was out Jonathan Stead broke down the right and beat Hughes for pace before driving a low shot straight at Shay Given.
Two goals to the good, United lacked their early urgency after the break and looked content to hang onto what they already had, while struggling Rovers saw their frustrations get the better of them on a number of occasions.
Good work from Bellamy on the edge of the box saw a rare chance, with the forward cleverly playing in Kieron Dyer, but the England midfielder could not improve his dreadful scoring record as his right-foot shot was tipped over by Friedel.
The next breakthrough came from United, with unsung hero O'Brien sending the Magpies into a 3-0 lead in the 83rd minute.
The ball eventually came out to Bowyer after a free-kick was knocked away and the Londoner found O'Brien near the byline. The Republic of Ireland defender then beat Matteo before shooting past Friedel from a tight angle.
James Milner then replaced Dyer, booed on his last home appearance but left alone this time round, as Newcastle ran down the clock. Patrick Kluivert remained on the bench while French teenager Charles N'Zogbia was brought on in injury-time for a brief debut.