City hammer 10-man Newcastle
David Silva took just six minutes to open City's account with a close-range header.
It was not entirely a trouble-free night for Pellegrini as he lost skipper Vincent Kompany to a groin injury.
Yet, compared to opposite number Alan Pardew, the Chilean's problems are minuscule.
And when he sees the television replays, the Magpies chief should be equally annoyed with Steven Taylor.
Inexplicably, Taylor deliberately caught Aguero round the side of his head with a swing of his arm, right in front of referee Andre Marriner.
It was an obvious straight red card and considering the visitors were already two goals down, left them with no chance of salvaging anything from a sorry evening.
Having been forced to wait 48 hours to enter the battle, during which time their main title rivals had secured comfortable victories, City seemed intent on making a statement.
Aguero had an early shot saved, Dzeko looked lively and Silva schemed.
Their own hopes hampered by the bid for Cabaye which triggered the Frenchman's return to the north-east because he was not in the right frame of mind to play, Newcastle wobbled.
And when Taylor turned Dzeko's near-post cross into the path of Silva, the little Spain star nodded home from close range.
As it happened, City's second came straight down the middle of the pitch.
Skipper Kompany put the visitors' defence on the back foot with an incisive pass to Dzeko, who caught Newcastle by surprise by flicking the ball straight on to Aguero.
His quick thinking allowed him to get half a yard in front of Taylor, which was all the room he needed to bury a precise shot into the bottom corner.
Amid a flurry of yellow cards Cheick Tiote brought a rare save out of Joe Hart with a long range effort before Dzeko headed Aguero's cross wide at the other end.
If Pardew was contemplating the swings and arrows of misfortune in the minutes ticking down the interval, he must have been incredulous at Taylor's early exit.
As he had also lost Jonas Gutierrez to injury, it was about as bad a 45 minutes as Newcastle could have imagined.
Within five minutes of the restart it had got worse.
Initially it appeared Newcastle had been reprieved thanks to a brilliant save from Tim Krul to deny Dzeko.
The hosts maintained their pressure, though.
And after Debuchy had fouled Aguero on the edge of the area, Toure curled a superb free-kick into the top corner.
Silva went close from a pass by Fernandinho, who was outstanding on his debut, then Dzeko was denied by Krul again.
Nasri's introduction in place of Aguero on the hour underlined the offensive strength Pellegrini has at his disposal, with Stevan Jovetic not even making the bench due to a minor knock.
At the back it is a different matter, though.
Not that it made any difference to the outcome as Nasri evaded the attentions of Debuchy to slot home City's fourth.
Dzeko went close again before Alvaro Negredo was handed his debut, the former Sevilla man having a goal incorrectly ruled out for offside in the dying stages.