Sergio Aguero scored twice as Manuel Pellegrini's men roared to victory at the Etihad Stadium with a magnificent late free kick from Wayne Rooney scant consolation for Untied.
The Argentina international was joined on the score sheet by Yaya Toure and Samir Nasri as the home side ran riot to climb to third in the Premier League table despite a terrific late consolation strike from Wayne Rooney.
The absence of Robin van Persie from Untied's squad made headlines, with the prolific Dutchman omitted with a groin strain. And, although the club was boosted by the return of Danny Welbeck, it was faced with the unenviable task of keeping an opposition pairing of Alvaro Negredo and Aguero quiet at the other end.
The chances of doing so appeared slim in the opening exchanges, as City began with impressive fluency despite the frenetic nature of the occasion.
The home side was rewarded for its endeavor after just 16 minutes when Aguero opened the scoring with a fabulous left-footed finish from inside the box. The Argentinian had plenty of work still to do after Aleksandar Kolarov had picked up the ball from Nasri on the overlap before crossing, but he controlled his volley beautifully to give his side the lead.
Kolarov's adventurous running from fullback caused problems again a few moments later, as the Serbian went down in the area following a challenge from Chris Smalling, but referee Howard Webb showed little interest in awarding a penalty.
City continued to dominate possession, with the frustration of United clearly evident when Rooney picked up a needless booking. The England international was given short shrift by the dominate City center back pairing of Matija Nastasic and Vincent Kompany in the aftermath, and Antonio Valencia's woeful effort from the edge of the box was the nearest United went to getting back into the game.
The club's hopes of taking anything from the game were severely dented on the stroke of halftime, as Negredo rose highest to flick on a corner and the unmarked Toure reacted quickly to divert the ball in off his knee from close range.
Moyes could at least take solace from the fact that the interval offered an opportunity to disrupt City's dominance, but just two minutes into the second half City grabbed a third. Negredo was the provider again, the Spaniard holding up the ball brilliantly under the attentions of Nemanja Vidic in the box before turning and teeing up Aguero for a close-range volley he could hardly miss.
City fans already in dreamland saw their day get even better just three minutes later, as Kompany's rampaging run from the back ended in a lofted cross that Nasri emphatically turned home at the back post.
The home side was happy to concede possession to United and attack on the counter given the size of the lead, but a long-distance effort from Marouane Fellaini, which Joe Hart easily kept out, was the best the visiting team could muster despite controlling the ball for long periods.
United's day was perhaps best summed up by a flurry of activity in the opposition goalmouth that saw Patrice Evra hit the post and Rooney somehow denied by the legs of Hart when his well-struck effort from inside the box looked bound for the back of the net.
The former Everton striker would get his goal eventually, however, curling in brilliantly from a set piece to add some respectability to the scoreline for Moyes' side.