City's title defence had crumbled heading into the match amid a run of five defeats in seven matches across all competitions, but the champions briefly displayed their fluent best in the early stages - Sergio Aguero's seventh goal in derbies after seven minutes the reward.
The direct, high-tempo approach United have found success with in recent weeks provided their route back into the match, with Ashley Young levelling before supplying the ammunition for Marouane Fellaini to give the hosts a 27th-minute lead.
Although Louis van Gaal's men were fortunate to be ahead at that stage, they proceeded to dominate their neighbours, who slipped into the kind of lethargic performance now synonymous with their 2015 efforts - heaping pressure on Manuel Pellegrini.
Juan Mata, the hero of United's recent triumph at Anfield, added a third midway through the second half amid strong suspicions of offside and Chris Smalling put the game beyond doubt, with Aguero's late strike - his 100th for City - providing scant consolation for the visitors.
United sit four points clear of fourth-placed City, who face a battle for UEFA Champions League qualification with their season on the brink of total collapse.
Smalling - sent off in United's 1-0 loss at the Etihad Stadium in November - returned from illness to line up in the home defence, with Marcos Rojo dropping to the bench.
City's backline was boosted by captain Vincent Kompany passing a late fitness test.
Despite their wretched recent form, City settled quickly and Jesus Navas raced clear of the United defence on the end of Martin Demichelis' lofted pass, but fellow Spain international David De Gea stood firm to deny him.
Pellegrini's team pegged their opponents back thereafter and, in a move that echoed the duo's combination play in City's famous 6-1 win at Old Trafford in October 2011, James Milner's reverse pass picked out David Silva to set up Aguero for a simple finish.
The visitors pressed forward to increase the damage, but United were back on terms after 14 minutes, Young scrambling home Ander Herrera's low cross at the second attempt.
Young turned then turned provider, combining cleverly with Daley Blind on the left flank and hanging up a cross for Fellaini to power past Joe Hart at the back post.
Fellaini's muscular presence caused City a persistent problem and Pablo Zabaleta made a vital headed clearance to deny the Belgium international a second in first-half stoppage time.
Kompany - who was booked for a rash lunge on Blind late in the first half - made way at the break due to further injury problems, meaning a first derby appearance for Eliaquim Mangala.
United came close to a third in the 52nd minute as Hart pushed a Wayne Rooney free-kick out of the top corner and the England goalkeeper saved from Michael Carrick's follow-up amid a frantic penalty box scramble.
City's early poise had faded to a distant memory by the time United made the points safe in the 67th minute - Demichelis out of position as he ceded possession to Blind, who found Rooney to send Mata scampering through for his eighth league goal of the season.
Questions over Pellegrini's position in the Etihad Stadium dugout are now sure to increase, and the scrambled mindset of his players was thoroughly exposed when Smalling was granted ample room to head home Rooney's free-kick amid further Old Trafford delirium.
Aguero then tucked home Zabaleta's 89th-minute cutback to reach his milestone on arguably the bleakest day of his City career.
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