The Blues started brightly but couldn’t breach a makeshift home defence during a frustrating 90 minutes on Merseyside and now lead the table on goal difference only from Manchester United.
This was never going to be a walk in the park for the Premier League leaders.
Past meetings between these two sides suggest Moyes takes particular pleasure in stoking his team up when faced with City. The reason behind that is unclear – the Joleon Lescott transfer, the touchline spat with Roberto Mancini a couple of years back – who knows?
But when his mid-table team take to the pitch against the Blues, they have been like men possessed and each meeting seems to be treated like a cup final with the vociferous home support completely in-tune with their heroes - and this clash was no different.
It’s now, just three wins in 30 visits to Merseyside, suggesting the jinx is as bad on both sides Stanley Park – but the carrot of a first double over the Toffees for more than 30 years was incentive enough for Mancini’s starting XI who began the night three points clear of the pack.
Vincent Kompany returned for City after serving his four-match ban, but the Toure brothers and suspended Mario Balotelli were absent.
The skipper couldn’t have timed his return any better with his team entering a period of games where the points could be plentiful and, if a first top-flight title since 1968 is to be achieved, the Blues were well aware they couldn’t afford too many slip-ups.
Both sides could have scored inside the first ten minutes with Lescott clearing Stracqualursi’s header off the line and then Micah Richards saw a low drive saved by Tim Howard at the near post.
Neither team created anything clear-cut for the next half-hour until Samir Nasri smacked a 25-yard howitzer against the underside of the bar with Howard beaten all ends up.
Moments later the crowd were treated to the bizarre sight of a pitch invader handcuffing himself to Joe Hart’s post for five minutes before play finally resumed when he was cut free by the police – and presumably placed in handcuffs again straight after.
As City tried to get a grip of the resilient hosts after the break, several half-chances went begging before the Toffees finally broke the deadlock on the hour.
Dzeko was beaten to the ball by Marouane Fellaini on the halfway line and from the resulting attack, Gibson fired Everton ahead from the edge of the box with a shot that took a wicked deflection off Gareth Barry.
It hadn’t really been coming, but it left the Blues with a mountain to climb and one, ultimately, they weren’t capable ascending on the night .
City poured forward in the closing stages, desperate for a break-through. Aleks Kolarov saw a cross strike Phil Neville’s arm in the box, but Peter Walton waved strong appeals away.
Then Royston Drenthe could easily have seen red for a nasty high challenge on Richards – but the Blues just don’t seem to get those decisions at the moment.
Now Mancini must rally his troops for Fulham on Saturday with a largely miserable January now confined to history.