The Australian rose above Micah Richards and Pablo Zabaleta to nod the ball in beyond Joe Hart's grasp to break City hearts.
In what had been a closely contended game, with end-to-end action, the result might just have been deserved for David Moyes' men, who shaded Mark Hughes' side on the day with their impressive organisation and dedication to the task.
City had Micah Richards, Robinho and Elano back in the team at the expense of Tal Ben Haim, Darius Vassell, and Dietmar Hamann.
Everton made light of the absence of all their recognised strikers upfront by attacking City with purpose and organising well at the back. Cahill was their nominal frontman but it was Osman and Marouane Fellaini who had the best chances for the hard-working visitors before the matchwinning corner fell to the patient Cahill.
Osman had already tested Hart in the opening couple of minutes before Richards brought down Cahill on the edge of the D. Mikel Arteta's ninth minute free-kick rebounded off the crossbar and fell nicely for Fellaini but his lofted header landed on top of Hart's goal.
Everton were working hard and carving out real chances, but their lack of strikers betrayed them as Moyes watched first-half chances wasted by Steven Pienaar and Arteta, while a great chance of an added-time tap-in from six yards by Fellaini off Osman's cross was thwarted by some great goalkeeping by Hart.
By contrast, City did have their chances but their threat was mainly kept to a minimum by the regimented Toffees. It was 13 minutes before their first convincing chance on goal.
Shaun Wright-Phillips came closest to scoring, rattling Tim Howard's crossbar from Robinho's lay-off after 41 minutes, but Howard was never really tested by efforts from Benjani, Stephen Ireland or Robinho later in the game.
If City are to realise their ambitions of European football, Hughes will have to get the chequebook out or they will simply not deserve to dine at the top table of European football next season.