The Toffees were forced to field an unfamiliar line-up for this crunch tie between two of the Premier League's would-be Champions League gatecrashers.
Manager David Moyes was forced to shuffle his pack with Joseph Yobo, Steven Pienaar and top scorer Yakubu away at the African Cup of Nations.
To add to his woes, prodigal loan signing Manuel Fernandes did not complete his move in time and Andy Johnson was absent after sustaining a knock in training.
Sven-Goran Eriksson had no such worries, welcoming midfielder Elano back into the fold and only missing Michael Johnson through injury.
Michael Ball and Richard Dunne returned together for the first time to the club they began their respective top-flight careers.
Both sides laboured to stamp any authority in a ragged opening period with the first real action coming in the 15th minute.
Mikel Arteta's corner sparked confusion in the City defence, but ultimately Victor Anichebe headed well over while under pressure in front of the City goal.
Tim Cahill missed a glorious chance to put the home side ahead after good work by Anichebe.
The youngster teed up the Australian whose first shot was parried by Joe Hart and then ricocheted back out as James McFadden challenged the goalkeeper, but Cahill's return shot from the left sailed over the bar from ten yards out.
Everton were gradually finding their feet and it was not surprising when they took the lead in the 31st minute.
Defender Joleon Lescott escaped the attention of the static Elano to tap in Arteta's low cross from three yards out after Phil Neville picked the Spaniard out on the right.
Everton kept the tempo up after the goal, restricting City to an Elano free-kick and a Vedran Corluka long shot as their only real attempts on Tim Howard's goal.
City started the second period much brighter with Everton sitting much too deep.
Three corners in as many minutes should have yielded better rewards for the visitors as they pinned the Toffees into their own half.
Both teams made changes with half an hour to go as Nery Castillo and Dietmar Hamann were replaced by Rolando Bianchi and Gelson Fernandes, while young striker James Vaughan came on for McFadden for the home side.
Everton threatened sporadically on the counter-attack with Arteta, Vaughan and Cahill linking nicely without any real penetration, but Eriksson would have been dismayed that his side lacked any real threat despite having the bulk of possession in the second period.
Howard did well to secure Everton the points at the death after he managed to smother Martin Petrov's fierce drive.
The fact that this was City's first and last shot on target in the entire 90 minutes tells its own story.