David Moyes' side were unable to breach a well-organised Swansea defence on Saturday, as it finished goalless at Goodison Park.
Everton were certainly the aggressor throughout the contest, hitting four times as many shots as their visitors, but were unable to find a way past Michel Vorm.
Here's a look at how Moyes' side fared individually.
Tim Howard: 7/10
A spectator for long periods, Howard reacted well to divert a Michu effort onto his crossbar.
He was also tidy dealing with crosses and quick with his distribution.
Seamus Coleman: 8.5/10
Coleman stood out as Everton's best player, continuing his fine form since his recent return from injury.
From right-back he was a continual presence in attack, marauding forward at pace, giving Ben Davies a particularly testing afternoon. He also looked far more confident when attacked one-on-one at the back.
Leighton Baines: 8/10
Despite being slowed by an ankle injury and closely tracked by Angel Rangel, Baines was still one of his side's top performers, laying off an impressive seven chances for others.
His delivery from set-plays were high-class and should have been capitalised on more than once.
Phil Jagielka: 7/10
A deserved clean sheet for Jagielka, who looked assured throughout, generally keeping Swansea's attackers quiet—although he should have scored from one of Baines' superb corners.
Given his side's superiority, he was in possession more than any other player and distributed nicely from the back at 87-percent accuracy. He was also far better with his longer passing than in recent weeks, finding a man 19 times from 24 attempts.
Sylvain Distin: 7/10
As with Jagielka, Distin's contribution warranted a clean sheet, but he was equally fallible at the other end of the field, wasting a great opportunity to hit the target.
In defence he was particularly imposing in the air, not losing a single aerial duel all game, and he prevented the visitors gaining any kind of meaningful possession in and around the box.
Phil Neville: 6/10
This was not the kind of game Neville was ever likely to impress in. He generally handed possession over to Osman, passing forwards just 17-percent of the time.
He organised those around him well enough to fend off most counter-attacks and mopped up several loose passes, but was rightly withdrawn for a more attacking presence.
Leon Osman: 7/10
On his 10th anniversary at the club, Osman moved the ball around well and tried to up the tempo without ever being as penetrative or incisive as in recent weeks.
He also was not as accurate in the final third as he's been this season and should have done better with a first-half header.
Victor Anichebe: 6.5/10
Full marks for application, though little for impact from the Nigerian, who struggled to make an impression from a wider berth.
Too often he didn't link up with an overlapping Coleman and was not as much of a presence in and around the box. He is better as the front man or coming in off the left than playing right.
Steven Pienaar: 7.5/10
Pienaar moved the ball well and created more chances from open play (four) than any other player, although he passing was not as consistent as it's recently been.
He still appeared Everton's most likely avenue of production despite a more congested left side causing him to roam around in search of space.
Marouane Fellaini: 7/10
Fellaini put in a strong performance without managing to impact the scoreline.
He won possession more than any of his teammates, ran further than anyone and was almost unbeatable in the air, allowing Everton instant possession in dangerous areas.
He adapted well when positioned as an orthodox midfielder late in the game.
Nikica Jelavic 5.5/10
His teammates were unable to present him with a glaring opening, but the Croatian will still rue several fluffed half-chances.
Who was Everton's best performer?
He failed to find the target with any of his five shots, again appearing rushed, and was not as effective as he's been in the past two fixtures at recycling possession or creating chances.
Steven Naismith: 5/10
Spent a lot of time running and is clearly an industrious player but made little contribution in the final third of the field, which would have been his task when introduced.
He continues to struggle maintaining his influence for sustained periods, drifting out of games far too much.
Apostolos Vellios: n/a
Created a chance late-on but wasn't on the pitch long enough to make an impression.