After the joy of six comes the glee of three. Unlike the destruction of Manchester United, this was not a result that will be transferred straight to DVD, although it was a rather harder earned victory. By its end, the lead over Manchester United had been extended on goal difference while Chelsea lay nine points adrift.

Nevertheless, Vincent Kompany's hauling down of Kevin Doyle meant that Roberto Mancini will be without his captain for the next game.

Given that it was their first home game since the great enemy had been shattered in their own lair, the gloating was kept to a minimum. The half-dozen goals at Old Trafford were played on the big screens before kick-off but the only prominent banner mentioning six was the longstanding one declaring that "On the sixth day God created Manchester City", which, if true, is evidence of a divine sense of humour.

Having scored five in the Carling Cup at Molineux on Wednesday, there was a natural expectation this would be another command performance, another victory parade. However, for a side that had come to Manchester portrayed as sheep in Wolves' clothing, they had fought unexpectedly hard.

At half-time, Mick McCarthy said he could taste the frustration in the throats of the home supporters. No side since Birmingham last November has come to Eastlands in the Premier League and kept a clean sheet. Wolves were displaying the subtlety and negativity of a nightclub bouncer with a baseball bat in his fist.

"I thought rather a lot was made of that match against Manchester United, because they played for 44 minutes with 10 men and that is very hard," said the Wolves manager. "But at half-time, I heard the crowd and I thought there was a lot of anxiety and frustration. For a side coming here to generate that kind of atmosphere is a good sign."

If McCarthy nursed hopes of a successful fighting retreat, they were gone six minutes after the interval. That was probably predictable, although that it would be through a rank goalkeeping error was not.

Wayne Hennessy had made his first save, tipping a drive from Samir Nasri into the crowd, when the scoreboard registered one minute and 14 seconds and had denied Edin Dzeko in the kind of one-on-one the Bosnian had exploited in the surreal closing moments at Old Trafford. An outstretched boot, a well-timed tackle and the kind of unsophisticated shoulder charge McCarthy would have recognised from his own days at City had kept Wolves afloat and that kind of attitude just might have lasted.

Under those circumstances, a routine clearance ought to have presented few problems but Hennessy dawdled and when he did try to punt the ball forward, it collided with Sergio Agüero's legs and rebounded to Dzeko who chipped into an empty net. In all competitions there is nobody with more goals and none would be quite as gift-wrapped.

"Wayne was fabulous; he has been all season," said McCarthy. "There are no recriminations but what annoys me is that we had been doing fine and we gave the opposition the lead. Then there is another mistake and we are 2-0 down."

This time Hennessy managed to block David Silva's shot after Agüero had pulled the ball back but the rebound fell to Aleksandar Kolarov, who bundled his way between David Edwards and Richard Stearman the two covering defenders, and forced the rebound home.

That ought to have been that but Wolves continued to niggle away; sometimes with the kind of tactics that brought to mind Arsène Wenger's comments that there are some teams that would not look out of place on a rugby field. Sometimes they genuinely hurt City and when Adlène Guedioura delivered a shot from outside the box, Joe Hart could only parry it towards Doyle. Given what happened, Kompany should probably have let him score instead of dragging him down. What followed was inevitable and likely – the red card and a penalty converted by Stephen Hunt.

Just as he had last Saturday, McCarthy made a double substitution but while Swansea had crumbled at Molineux, City are made of rather more expensive, vastly more experienced material.

Mario Balotelli, who had been rewarded for his efforts at Old Trafford with a place on the bench here, broke away and fed Adam Johnson, whose shot displayed the kind of qualities entirely lacking in McCarthy's side. On Wednesday night in the Black Country, Johnson had reportedly refused to board the City bus because he felt Mancini's attitude towards him was so unremittingly harsh. Now he seemed keener to be with his team-mates.

• This article was amended to correct the length of ban Vincent Kompany will face, from three games to one