Edin Dzeko scored after just 42 seconds to put City ahead and the big striker struck again after the break before Yaya Toure rounded off yet another miserable night for Moyes.
Further questions will surely be asked about Moyes' ability to bring the glory days back to United.
There was no fortune about this victory from Pellegrini's team, who are now three points off the top of the Barclays Premier League with two games in hand on Chelsea.
If anything, it was a minor miracle that City did not win by four or five.
David Silva, Toure, Fernandinho and Samir Nasri overran and outclassed a weak United midfield and Dzeko - a surprise starter ahead of Alvaro Negredo - did the rest up front.
It seems, after all, that Pellegrini had a point when he said there has been only one club in Manchester this year.
United lacked confidence, tempo and cohesion. There was no cutting edge up front while the back line was exposed for its lack of pace, just as was the case against Liverpool.
Moyes made life easy for the visitors too. Antonio Valencia was left on the bench and Adnan Januzaj did not even make the squad, leaving United with no width at all.
Moyes placed his faith in Tom Cleverley as has been common in the big games this year, and once again the England midfielder failed to deliver.
Things could have been worse had Marouane Fellaini received the red card he deserved for an elbow on Pablo Zabaleta or had David de Gea not prevented Dzeko scoring his third with a superb save.
There were plenty of glum faces by the final whistle, and one of them was Moyes'. The statistics do not make for good reading for the Scot.
United are now guaranteed to end the season with their lowest points total in Premier League history.
They have been defeated in six home games for the first time since 1978 and they have now lost three successive derbies for the first time in 45 years.