Match ends, Everton 2, Manchester City 3.
Manchester City took a significant step towards claiming the Premier League title as they returned to the top of the table on goal difference with victory at Everton.
Liverpool were looking to their neighbours to do them a favour and beat City - and their hopes were briefly raised when Ross Barkley's spectacular early strike put Everton ahead.
City gathered their forces and goals from Sergio Aguero, who then went off with a groin injury, and Edin Dzeko put them ahead before the interval.
Bosnia striker Dzeko's second gave City a measure of comfort but Romelu Lukaku's header left them with an anxious last 25 minutes before they closed out a win that gives the perfect platform for their final home games against Aston Villa and West Ham.
Manuel Pellegrini's side were nowhere near their best, and were reduced to some fairly blatant time-wasting near the end, but it was about getting the job done and this was mission accomplished.
It was a disappointing conclusion to Everton's fine first season under manager Roberto Martinez as their Champions League hopes were finally snuffed out in the battle with Arsenal, but they are now certain to finish fifth and claim the deserved reward of a return to Europe in the Europa League.
|Race for the Premier League title|
|Mon 5 May: Crystal Palace (a)||Sun 4 May: Norwich (h)|
|Wed 7 May: Aston Villa (h)|
|Sun 11 May: Newcastle (h)||Sun 11 May: Cardiff (a)||Sun 11 May: West Ham (h)|
The pressure now switches to Liverpool and their difficult trip to Crystal Palace on Monday night, knowing City's result puts their fate outside their own hands barring some extraordinary goalscoring feats.
Much had been made of Everton's motivation to win, given that victory would lend such assistance to rivals Liverpool - but no-one could mistake Barkley's intent as he scored a magnificent opener after 11 minutes.
Leighton Baines and Steven Naismith played a part, but all the credit must go to Barkley as he curled an instinctive finish high past City goalkeeper Joe Hart from 25 yards.
Barkley troubled City again with another surging run that had Everton appealing for a penalty as he tangled with Vincent Kompany but referee Lee Probert was not interested.
City, who had been pedestrian so far, were suddenly prompted into life and were soon level as Aguero picked up Yaya Toure's pass and beat Everton goalkeeper Tim Howard at his near post.
It was the Argentine's last action as he limped off with what looked like a groin muscle injury, a concern for both club and country with two vital title games and a World Cup to come.
Fernandinho came on and City finally settled, taking the lead just before half-time when Dzeko rose to meet James Milner's cross and head past Howard, who moved late and was beaten low down.
Barkley was at the heart of all Everton's best moves and he almost created an equaliser right after the break with another surging run before setting up Naismith, who forced a vital fingertip save from Hart.
The importance of that save was emphasised seconds later when Dzeko stabbed home Samir Nasri's cross from six yards. The scenes of celebration on the City bench told the tale.
Everton were struggling to impose themselves on City but gave themselves - and Liverpool - hope with 25 minutes left when poor marking allowed the previously dreadful Lukaku to send a diving header past Hart via the post from Baines' cross.
From looking so comfortable, City suddenly looked uneasy and there was fury among the home fans when Dzeko lay motionless for minutes, without the medical team being called on, before finally getting to his feet and receiving a yellow card.
Barkley was at it again in the closing minutes, releasing substitute Gerard Deulofeu in the area but his shot was blocked by Hart's legs at the near post.
It was City's final moment of concern as they played out six minutes of stoppage time to clinch only their second win at Goodison in 15 visits. But more importantly for City it edged them closer to the title.
Everton manager Roberto Martinez: "There is a moment when Sergio [Aguero] is coming to the side and is trying to come off as he was feeling an injury and the next action he gets into a good position which leads to a goal [City's first].
"We were in total control and for us it was disappointing to concede that goal out of a bit of confusion with a player who needs to come off.
"The first chance of the second half, Joe Hart made the save of the season. They went to the other end and we conceded a goal in a very important moment - I thought that was the turning point."
For a gallery of photos from Saturday's Premier League action, head to the BBC Sport Facebook page.
- 6JagielkaSubstituted forDeulofeuat 66'minutes
- 21OsmanSubstituted forMcGeadyat 83'minutes
- 26DemichelisBooked at 66mins
- 8NasriSubstituted forSilvaat 74'minutes
- 42Y TouréSubstituted forKolarovat 66'minutes
- 14García FernándezBooked at 39mins
- 16AgüeroSubstituted forFernandinhoat 28'minutes
- 10DzekoBooked at 83mins
- Lee Probert
- Shots on Target
Second Half ends, Everton 2, Manchester City 3.
Foul by Aiden McGeady (Everton).
Fernandinho (Manchester City) wins a free kick in the attacking half.
Corner, Manchester City. Conceded by John Stones.
Attempt blocked. David Silva (Manchester City) left footed shot from outside the box is blocked. Assisted by Edin Dzeko.
Foul by James McCarthy (Everton).
Edin Dzeko (Manchester City) wins a free kick in the defensive half.
Corner, Everton. Conceded by Joe Hart.
Attempt saved. Gerard Deulofeu (Everton) right footed shot from a difficult angle on the right is saved in the centre of the goal.
Delay over. They are ready to continue.
Substitution, Everton. Aiden McGeady replaces Leon Osman.
Edin Dzeko (Manchester City) is shown the yellow card for a bad foul.
Delay in match Edin Dzeko (Manchester City) because of an injury.
Ross Barkley (Everton) wins a free kick in the defensive half.
Foul by Edin Dzeko (Manchester City).
Substitution, Manchester City. David Silva replaces Samir Nasri.
Attempt blocked. Martín Demichelis (Manchester City) right footed shot from outside the box is blocked.
Attempt missed. Edin Dzeko (Manchester City) header from the centre of the box misses to the right. Assisted by James Milner with a cross.
Attempt missed. Fernandinho (Manchester City) header from the centre of the box misses to the right. Assisted by Samir Nasri with a cross following a corner.