City took the lead on just five minutes after Ruben Dias took full advantage of some questionable Toon defending to head the visitors in front from close range.
They doubled their lead on midway through the first half courtesy of an excellent solo-run and finish from Joao Cancelo.
Story of the game
After the 3-1 defeat to Liverpool in midweek, Eddie Howe made five changes to his Magpies team with Ciaran Clark, Matt Ritchie, Joe Willock, Miguel Almiron and Callum Wilson all coming in to the side.
This match – dubbed as the 'Gulf Derby', the 'El Cashico', the 'Oil Derby' and 'Saudi Arabia vs Abu Dhabi' for obvious reasons – got off to the worst possible start for the hosts, as they fell behind after just five minutes.
It was all so avoidable for Newcastle, a goal that game to fruition from a botched clearance from Martin Dubravka that resulted in a City corner.
The Magpies momentarily cleared the ball but Cancelo latched onto a lofted pass and hooked the ball across the six-yard area. It looked like a routine header away for Clark– his first involvement since his moment of madness against Norwich – but instead he ducked and left Ruben Dias the simple task of heading the ball home from point-blank range.
Newcastle did respond well to going behind, and went close twice to equalising.
Just after Joelinton took aim from 20-yards and narrowly put the ball wide, Isaac Hayden stole the ball off Kevin De Bruyne in his own penalty area and the ball fell to Ryan Fraser who was denied by a goal-line clearance by Aymeric Laporte – but it was deemed Hayden fouled the Belgian.
10 minutes after that good spell for The Magpies, City doubled their lead, and it was all too easy once again for the Champions.
Cancelo drove with the ball from the half-way line, leaving two Toon players in their wake before lashing the ball into the top-left corner.
If Newcastle thought they didn't get the rub of the green off Mike Dean at Anfield in midweek, they had seen nothing until today, when they were denied a stonewall penalty by Martin Atkinson three minutes after going two behind.
Fraser was wiped out by Ederson in the area, but somehow, The Magpies weren't awarded a penalty by the referee, or VAR.
The reason why? 'Cancelo came away with the ball', which means it is now – apparently – acceptable to take wipe an opposition player out, as long as one of your teammates comes away with the ball.
With the last chance of a half masked by injustice, City came close to putting the game to bed on the stroke of half-time, but Gabriel Jesus' effort whistled past the post.
Mahrez's volley and Sterling's strike secures three points for the Champions
The visitors came out of the blocks early after the interval, and it took a remarkable point-blank stop from Martin Dubravka to deny Jesus' header of rippling the back of the net.
But it didn't take the visitors long to get their third goal.
Oleksandr Zinchenko broke down the left-hand side and cross towards an unmarked Riyad Mahrez at the back-post, who calmly volleyed the ball into the bottom corner with the side of his boot to put this tie beyond any doubt.
The Algerian was denied by the offside flag at first, but VAR – now seemingly working again – intervened to give him his 50th goal in a City shirt.
Guardiola's men nearly got their fourth minutes later, but Laporte's effort at the back-post was wide of the mark.
Newcastle came close to a consolation goal eight minutes from time, but Wilson's header was tipped over-the-bar by Ederson.
To ensure this really was the nightmare before Christmas for the hosts, four minutes from the final whistle, Jesus broke down the left-hand side and played a ball along the goal to Sterling, who had the simple job of stabbing the ball into an empty net.
The resounding win for City ensured they went four points clear at the top of the table before Liverpool kicked off later in the afternoon.
Newcastle: Dubravka; Murphy, Lascelles, Clark, Ritchie; Almiron, Joelinton, Hayden, Willock, Fraser; Wilson. (4-5-1)
Manchester City: Ederson; Cancelo, Dias, Laporte, Zinchenko; Rodri, De Bruyne, Silva; Mahrez, Jesus, Sterling. (4-3-3)