It was a night when one man brought handcuffs and Manchester City played as though in a straitjacket. They will go into February top of the league, encouraged by the fact that the last eight titles have been won by the team leading at this stage, but this was a dishevelled, almost perplexing performance on an evening that will otherwise be remembered for a pitch invader handcuffing himself to the goalposts.

Never before has a Premier League match been interrupted by a middle-aged man protesting about Ryanair's recruitment policies, on the apparent basis that his daughter did not get a job with the airline. Play was suspended for four minutes while a dozen or so stewards and police officers worked out how to release him, the solution arriving when a member of groundstaff found some bolt-cutters. In hindsight, City probably regret the game was not abandoned.

It was a surreal subplot to a match in which they rarely looked like a team good enough to challenge for the title. They have found Everton the nearest thing to a bogey club in recent years and Darron Gibson's second‑half winner, his first goal since signing from Manchester United last month, means they have won only two of their last 15 league games at Goodison.

Taking into account the fact Everton were missing their first-choice centre‑halves and had six outfield players on their bench with an average age below 20, it was worrying in the extreme for a side with City's ambitions. If they are going to hold off Manchester United, now level on points, they are going to need a dramatic improvement between now and May regardless of Mancini's insistence that it was all his fault.

The City manager said he had prepared the team badly and been guilty of under-estimating their opponents. "I thought it may be easier," he said. "I didn't prepare us well and it is important for me to know my mistakes because I can't do the same in the next game. I should know here it is never easy – never.

"We had played well against Tottenham in our last game, we had won our last three Premier League games and Everton were missing three or four players. It was a bad night for me. It's going to be impossible for me to sleep tonight."

City had plenty of possession but did little with it. Their full-backs seldom broke forward in the usual manner, the forwards struggled and, faced by a team that are renowned for effort and togetherness, they did not always demonstrate the same competitive spirit. However much he defended his team, Mancini will have noted the way Gareth Barry turned his back on Gibson's shot for the game's decisive moment.

The story of City's failures should not overshadow the way Everton overcame the absence of Phil Jagielka and Sylvain Distin in the centre of defence to keep out the division's leading scorers. This was David Moyes's 150th league victory. "Arguably it might have been the best," he said. "The team we had, the players missing, we had to defend for long times but it was a great effort. That's as good as it has been at Everton for a long time."

Their performance was epitomised by the way Tony Hibbert, a right-back by trade, handled his move to centre-half, despite giving away six inches to Edin Dzeko. John Heitinga was equally impressive and, though the home team seldom threatened City's goal, there was plenty more to impress Nikica Jelavic, watching from the stands after his £6m move from Rangers.

City will look back on the moment, with the game goalless, when Samir Nasri thumped a 30-yard effort against the joint of post and crossbar but, in total, they managed only three shots on goal. The passing was nowhere near as crisp as usual. Even in the half-hour when they were losing, the increased pressure never really amounted to anything.

David Silva had little patches and Sergio Agüero flitted in and out but even when they were playing the more cohesive football there was little at the end of it. They will reflect on a couple of penalty claims, one for Phil Neville's handball and one for Tim Howard clattering into Joleon Lescott's back, rather than a succession of missed chances.

Moyes could also cite the moment, inside the first five minutes, when Denis Stracqualursi's downward header beat Joe Hart only for Lescott to clear on the line. That came from a straightforward corner and was the first indication that, even with Vincent Kompany back from suspension, City were susceptible.

They were punished after 59 minutes. Gibson has always had a powerful shot and when Landon Donovan laid a short pass into his path the crowd implored him to have a go. His strike took a decisive flick off Kompany to fly past Hart.

Should Manchester United go on to win the league, their former player will have made a telling contribution.