Carlos Tevez provided City with some Christmas cheer before kick-off but the Toffees denied them the present they really wanted.
Instead of sitting top of the table on December 25 for the first time since 1929, they remain in third, beaten by the Toffees once more who registered their fourth successive win at Eastlands.
First-half efforts from Tim Cahill and Leighton Baines were enough for the visitors, who defended valiantly once they had gained the initiative and secured their first win since October.
Not even the needless dismissal of Victor Anichebe could stop them as Mario Balotelli hit a post after Yaya Toure's deflected effort had pulled one back.
It meant there was no dream end to an evening that began with a statement confirming Tevez's intention to remain at City - for the short-term at least - after a week of bad blood between player and club.
How quickly football can change moods.
Thirty minutes before kick-off, Mancini was all smiles, explaining what a fillip it was that Tevez had withdrawn his transfer request and how the City family were now looking forward to the future with confidence.
Less than an hour later, he was angrily booting over a set of neatly-arranged water bottles, gesticulating wildly at his disappearing defence, not knowing whether to stand or sit such was the height of his agitation.
It is not as though City were without warning.
Everton's last three visits to this ground had ended in victory, the last two of which had involved a goal from Cahill.
That the Australian should find the net with a trademark header, after only four minutes, having been left completely unmarked by Vincent Kompany could explain Mancini's arm-waving reaction.
In fairness to Kompany, he was gambling to try and block a potential Seamus Coleman lay-off to Jack Rodwell.
Unfortunately for the hosts, in doing so, he offered Cahill a far easier opportunity as Coleman picked him out inside the six-yard box.
Everton's second came when Pablo Zabaleta was off the field having stitches inserted in a wound that followed a clash of heads with Cahill.
The bitter pill for City came in the form of Baines and Anichebe combining down the wing Zabaleta was supposed to be patrolling and Cahill providing the lay-off for a precise finish from Baines.
It was superb simplicity, although the beauty was lost on Mancini as Baines wheeled away in glee.
For a side that had not won in seven games since October, it was a glorious half, which they defended with vigour.
Six blocks to six shots in one City barrage, Phil Neville getting in the way of a Zabaleta shot and Phil Jagielka stopping one from Kompany, both of which brought penalty appeals.
Aleksandar Kolarov also went close with a free-kick Tim Howard just managed to turn round the post as it threatened to creep in.
The Serb went close with a dipping shot at the start of the second period after David Silva had combined with Tevez to set him up.
But City were running out of ideas until Anichebe threw them a lifeline with his ridiculous red card.
The striker, who has refused to sign a new contract and was a surprise selection ahead of Louis Saha, could just about be excused for barging over Joe Hart as he challenged for a ball he was never quite getting to.
His needless trip of Zabaleta four minutes later was totally irresponsible as it earned an obvious second yellow card and left Everton to fight on with only 10 men.
For good measure, Anichebe threw his gloves at Mancini's feet before marching off down the tunnel.
Even with their numerical advantage, City still needed a massive slice of good fortune to get themselves back into the contest as Yaya Toure's wayward shot struck Jagielka and bounced in.
That Jagielka was forced off through injury merely compounded Everton's woes, although City had gone agonisingly close to grabbing an equaliser when Mario Balotelli sprinted on to Toure's excellent pass, chipped Howard but saw the ball bounce back off the post.
Howard recovered his ground quickly enough to deny Tevez's close-range effort with the follow-up.
City piled forward at the end, but their only notable entry into referee Peter Walton's notebook was for the dismissal of Kolo Toure for two injury-time bookings.