Vincent Kompany doubled the lead on the cusp of half-time with a powerful header from Martin Petrov's corner.
Again, the marking was poor as Kompany easily outmanoeuvred Tal Ben Haim before powering an unstoppable header past James.
His request was echoed by QPR's Joey Barton, who grew up on Merseyside, and Manchester City captain Vincent Kompany.
That spell of pressure was rewarded just before the half-time whistle when Vincent Kompany found Vieira 20 yards from goal.
Kompany then fired wide in first-half injury time after Milner's poor cross on a counterattack was pushed out to him by Cech.
But Kompany was also cautioned for becoming involved in the ensuing melee.
And City made the points safe on the stroke of half-time when Vincent Kompany powered a header past goalkeeper David James from Martin Petrov's corner.
Nosworthy neatly fed Henderson in space on the right, and from his cross substitute Jones got ahead of Vincent Kompany to head in from six yards.
The little man was giving away height, weight and reach to Kompany but he soared magnificently above the defender to send a flying header over Hart.
Unfortunately for City, they were again undone by a mistimed tackle - Kompany felling Fabregas just inside the area with the Spaniard dribbling away from goal.
Mancini said he planned to appeal the decision, even though an unsuccessful petition to the Football Association could mean Kompany is banned for four games instead of three.
Carlos Tevez and David Silva struck in the first half with Vincent Kompany and an own goal by Newcastle defender James Perch completing a resounding victory for Robert Mancini's team.
In May's EPL finale, Barton was sent off for elbowing Carlos Tevez, then kicking the striker's fellow Argentine Sergio Aguero before appearing to aim a headbutt at City captain Vincent Kompany.
The only blot on City's day came when captain Vincent Kompany was sent off for a sliding two-footed tackle on Jack Wilshere, though the Belgium defender appeared to win the ball.
Striker Emmanuel Adebayor and defender Vincent Kompany were seen arguing during Saturday's defeat, while Yaya Toure and Milner were understood to have had a disagreement at the interval during the defeat by Arsenal.
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City upped the pressure and absolutely peppered the Everton goal with shots for a short spell after the half hour, but the Toffees somehow kept out David Silva, Vincent Kompany and Mario Balotelli.
Florent Malouda drilled a thunderous long-range strike narrowly over the crossbar, Shay Given palmed clear from Joe Cole, Didier Drogba headed over and Vincent Kompany almost sliced an attempted clearance into his own net.
Tevez did not have to wait long to add his 19th goal of the season, rounding off a neat build-up involving Vincent Kompany and Silva by hurdling a sliding Reid challenge and firing confidently home.
Geovanni showed true Brazilian flair with an aerial volley that flew narrowly over the crossbar but he pulled Hull level on the hour mark when his free-kick found the net after a deflection off Vincent Kompany.
Chelsea's first chance came in the 23rd, when an inswinging free kick was only cleared out to Eden Hazard, whose bouncing shot from outside the area went over Pantilimon but was cleared off the line by Vincent Kompany.
Martins swung a cross in but, as Dunne cleared, the ball deflected off Vincent Kompany and Ben Haim into the path off Ameobi who chested the ball forward and finished awkwardly for his first goal in over two years.
The full-back latched on to John Utaka's intelligent back heel inside the box and rifled his shot into Kompany as the ball looped over Given and on to the crossbar, with Ireland clearing the danger with Danny Webber poised to pounce.
The need for City to add to the squad in January has been underlined ahead of the trip to Hull City on Sunday, with Richard Dunne, Gelson Fernandes and Michael Johnson joining the list of absentees, though Vincent Kompany should be fit to return to action.
Former City defender Sylvain Distin headed Everton's equaliser from Mikel Arteta's free-kick after 65 minutes with goalkeeper Joe Hart at fault - and as Roberto Mancini's men rocked under increasing pressure, Leon Osman rose spectacularly to beat City captain Vincent Kompany and head the winner seven minutes later.
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