Pep Guardiola made just one change from the side that dismantled West Ham nine days before with Claudio Bravo replacing Willy Caballero in goal.
The pressure was on the Blues before a ball had even been kicked with Arsenal, Chelsea and Spurs all winning handsomely 24 hours earlier - the pace at the top continues to be relentless.
City started confidently and before long were dominating possession with some excellent movement, particularly from David Silva, Kevin De Bruyne and Raheem Sterling.
The first real talking point of the game came on 13 minutes when Sterling raced onto a De Bruyne cross but as he tapped it past Joel Robles, a combination of the Everton keeper and a sliding Leighton Baines challenge felled the City winger.
TV replays proved he’d been caught, but referee Mark Clattenburg saw no offence and play was waved on.
With Everton gradually sinking further and further back, it looked like a matter of time before City went ahead, but a combination of hesitancy and occasional over-elaboration meant all the Blues’ excellent build-up often fizzled out where it mattered most.
De Bruyne spotted Silva in acres of space in the box on 27 minutes but the Spaniard was closed down quickly by Robles when a first-time volley might have been the better option.
After 34 minutes of near complete domination, it was Everton who broke forward and opened the scoring – not the first time City have dominated without scoring and then paid the price.
Gael Clichy’s pass was cut out by Tom Davies on the halfway line and his ball to Kevin Mirallas whose cutback was driven into the back of the net by Romelu Lukaku.
It was cruel and against the run of play, but it is the price for profligacy in front of goal.
De Bruyne continued driving City forward and his low cross almost saw Sergio Aguero slide home the equaliser on 37 minutes and then Sterling sent a 20-yard shot inches past the post – but still the Toffees held on.
The half ended with Bacary Sagna’s header cleared virtually off the line – the next presentable chance that cane to the Blues had to be converted if Pep’s team were to turn this game around.
As it was, within two minutes of the re-start, Everton had doubled their lead with their second shot of the game.
A series of mistakes allowed the ball to eventually find its way to Mirallas on the edge of the box and his low shot beat Bravo to make it 2-0.
It was always going to be a long way back for City from that moment on and the Blues, looking like the stuffing had been knocked out of them, struggled to resume the dominance and style they'd had in the opening period.
Everton added a third on 79 minutes when Tom Davies clipped the ball over Bravo to put a slightly flattering look on the scoreline.
But there was even worse to come as debutant Ademola Lookman added a fourth with virtually the last kick of the game as John Stones' clearance to a free deflection into the debutant's path to complete a miserable afternoon for Guardiola's side.
All in all, a day to forget.