Pep Guardiola's side dominated possession during the first half but lacked the clinical touch shown by Romelu Lukaku when he dispatched his 12th Premier League goal of the season from the hosts' only shot on goal during the opening 45 minutes.
It became two from two a little over a minute after the restart, with Lukaku and City's slipshod defence again to the fore as his Belgium international colleague Kevin Mirallas picked out the bottom corner.
Teenage midfielder Tom Davies crowned a majestic performance with a remarkable first senior goal 11 minutes from time and new signing Ademola Lookman came off the bench to add a fourth on his debut, ensuring Everton moved four points clear of West Brom in seventh – cementing their current status as best of the rest against the present worst of the elite,
City were aggrieved when Raheem Sterling was denied an early penalty but their lack of conviction in the final third and persistent vulnerabilities around their own box mean an aging squad appear increasingly likely to view a keenly contested title battle from a distance.
As Chelsea, Tottenham and Manchester United have composed imposing winning runs, City have won four and lost four of their past eight Premier League outings - form that makes for dismal reading ahead of next weekend's showdown with Spurs and their overall prospects of securing Champions League qualification.
Raheem Sterling enjoyed City's first clear opening, after Mirallas had seen a goal chalked off for offside, but opted to try and round Joel Robles, went to ground over the Everton goalkeeper's trailing leg and was frustrated in his penalty appeals.
The England winger did get a shot off on the end of Kevin De Bruyne's lofted pass, only to stab a volley directly at Robles.
The Spaniard was then out quickly to thwart countryman David Silva and, after absorbing mounting City pressure, the hosts hit the front in the 34th minute.
Davies collected Gael Clichy's wayward clearance and his measured pass sent Mirallas into space down the right channel to cut back for Lukaku to convert with nonchalant ease.
Sterling fizzed just wide from long range and right-back Bacary Sagna saw Davies clear his header off the line in first-half stoppage time as Guardiola's men reached the interval in arrears.
They began the second period in dreadfully lacklustre fashion and faced double the deficit within 62 seconds of the restart.
John Stones - barracked throughout on his return to his former club - cut out Lukaku's pass but Pablo Zabaleta was slow to react to the loose ball, leaving Ross Barkley to pick out Mirallas to finish unerringly having been played onside by Nicolas Otamendi.
City now lacked their earlier fluency, with scrappy passages of attacking play punctuated by some abject set-piece delivery.
Robles was on hand for smart saves to keep out Sergio Aguero and De Bruyne, by which stage Everton recording back-to-back Premier League wins for the first time since September was in little doubt.
Davies made sure in glorious style, collecting possession in his own half and turning inside Gael Clichy and Yaya Toure before picking himself up off the turf and dinking Barkley's return pass over Claudio Bravo for an unforgettable first senior goal.
And there was much mirth when Lookman was the beneficiary of a stoppage-time error by Stones, who was unlikely to receive any assistance from team-mates who seemed to have given up entirely as their manager suffered the heaviest league loss of his illustrious career.