Roberto Martinez's men saw their Champions League dream ended by the new Premier League leaders, who leapfrog Liverpool on goal difference with two games left to play
The league leaders looked in for a difficult afternoon and fell behind early to a stunning curling effort from England World Cup hopeful Ross Barkley.
|VIEW FROM GOODISON PARK
|By Paul Macdonald
Pre-match inclinations that Everton wouldn't be overly bothered if Manchester City collected the points and denied city rivals Liverpool the title were undone by Ross Barkley's fantastic opening goal and indeed the overall endeavour of the home side.
But to City's credit, they responded like potential champions. Edin Dzeko struck two invaluable goals to justify his continued inclusion in the side, while Joe Hart produced two saves of the finest quality to deny Steven Naismith and Gerard Deulofeu respectively.
It's a massive three points for Manuel Pellegrini and his team - surely now Premier League winners in waiting.
Romelu Lukaku responded with a header from a Leighton Baines cross to set up a nervy finish and despite the best efforts of Gerard Deulofeu, who forced a save from Joe Hart with a fine individual run, Roberto Martinez's side could not find an equaliser and saw their Champions League hopes ended.
City made an enterprising start, with Aguero often the architect, but Everton took a 10th-minute lead in sensational fashion.
Barkley, who impressed throughout, brought Goodison Park to its feet by whipping Steven Naismith's lay-off into the top corner from 25 yards.
Yaya Toure brushed Leon Osman aside to blast over after 16 minutes, while Barkley jinked past Javi Garcia and Martin Demichelis at the other end to prompt a magnificent last-ditch tackle from Vincent Kompany.
Perhaps inspired by their captain's heroics, City drew level in the 21st minute.
Centre-back Antolin Alcaraz was drawn towards Toure, who slipped a pass though for Aguero to blast beyond Tim Howard at his near post.
However, in the act of scoring, Aguero appeared to sustain another leg problem in an injury-plagued season and the striker was replaced by Fernandinho.
As half time approached Howard thwarted Dzeko from an acute angle but when the ball was worked out to James Milner the big Bosnian was on hand to head home from a pinpoint cross.
Everton had a glorious chance to draw level within a minute of the restart as Barkley stormed forward and Naismith shrugged off Pablo Zabaleta, but Joe Hart made a stunning low save to deny the Scotland international.
In a similar response to the one following Kompany's earlier brilliance, City streamed up field to give themselves breathing space.
Fernandinho sublimely controlled the attack and found Samir Nasri, whose low centre was turned in by Dzeko for City's 150th goal in all competitions this term.
Faced with the seemingly routine prospect of closing out a decisive win, City then faded badly and Lukaku reduced the arrears when he stooped to convert Leighton Baines' arching cross.
Bizarrely, City's defenders were then of greater use at the other end of the field, as Zabaleta and Demichelis went close to adding a fourth.
Lively Everton substitute Gerard Deulofeu rippled the side netting after cutting through the visitors with a brilliant jinking run.
A lengthy period of treatment for a shoulder injury to Dzeko brought about six minutes of stoppage time, but Manuel Pellegrini's side held on and are likely to guarantee a second league crown in three seasons by winning their remaining matches, at home to Aston Villa and West Ham.