Tim Cahill answered the call as an emergency striker to give Everton a dramatic victory at Eastlands.
Pushed up from midfield, he grabbed the vital goal deep in stoppage-time to stun City. It was no more than Everton deserved as they dominated the game for most of the 90 minutes.
Yet manager David Moyes lost his remaining striker Victor Anichebe before kick-off as he failed a fitness test on his back.
Everton almost took the lead as early as the sixth minute when Leon Osman skipped past two defenders and into the penalty area.
It was good skill by the midfielder but his effort went narrowly wide of Joe Hart's post.
There was another scare for City four minutes later when Micah Richards was penalised for a challenge on Cahill. Mikel Arteta delivered a superb free-kick from the edge of the area but it came back off the bar.
The rebound fell to Marouane Fellaini, who only succeeded in sending a close range header high into the crowd.
City responded and Stephen Ireland chipped the ball over the bar three minutes later after being released by Benjani Mwaruwari.
Fellaini, however, again showed a lack of confidence in the 18th minute with a wayward header from Arteta's corner.
Everton then made an unsuccessful appeal for a penalty in the 20th minute when Osman appeared to be hauled back by Michael Ball as Fellaini played the ball in.
Arteta was beginning to boss the midfield and sent in a thunderous drive from the edge of the area in the 28th minute that Hart did well to block with his body.
City hit back and Elano split the defence five minutes later and released Benjani. But the ball got stuck under the striker's feet and he was unable to take advantage of the opening.
It was a rare opening for City, who were struggling to find their rhythm in the driving rain.
Shaun-Wright Phillips then decided to take matters into his own hands and strode forward in the 41st minute. He delivered a rasping drive that beat goalkeeper Tim Howard but it skimmed the top of the bar and went over.
Fellaini almost made the breakthrough in stoppage time from inside the six-yard area but Hart made a superb block.
Then Lescott headed over when Osman swung in the corner from the left.
City against found themselves on the back foot in the 58th minute when skipper Phil Neville delivered a fine low cross from the right.
However Fellaini failed to get a vital touch and Pablo Zabaleta headed clear as Cahill waited to pounce.
Play switched back down the other end and Wright-Phillips sent in a cross that was cleared to safety by Neville.
Robinho was still struggling to make an impact as was Elano with Everton playing with confidence despite the home defeat by Aston Villa last Sunday.
Arteta was continuing to make things tick in the middle of the park while Cahill was putting in a hard shift in an attacking role.
Robinho came off with 10 minutes remaining after failing to make an impact and was replaced by Darius Vassell.
City have been scoring goals for fun at home but there was a lack of punch in their play and Jo headed off target following a cross from Wright-Phillips in the 87th minute.
Cahill then scored that late, late winner when he climbed above Richards to head home a corner from Osman.