After beating Cheltenham in the third round, the Toffees now travel to Bolton, hoping for a place in the last 16.
It's an interesting debate among fans over which is more important—Champions League qualification or silverware—but certainly at this stage the tie will be taken extremely seriously.
The FA Cup has provided the Toffees with several memorable moments over the years and here are five reasons why David Moyes' side are genuine contenders once again.
A factor that often breeds success is experience, and most of Everton's current squad are familiar with reaching the business end of the tournament.
The Toffees have had three Wembley trips over the past four years, via a 2009 final and a 2012 semifinal, and have enjoyed some impressive results during those cup runs.
Everton's dressing room should harbour an expectancy of going deep in the tournament.
Since this time last year, Everton have been on an impressive run in the Premier League.
They have been maintaining top-four consistency and have pulled off some major results against the best teams in the country.
All of the Premier League's current top four have been beaten by the Toffees, which will surely provide them confidence for this current tournament.
Given this lengthy period of consistency, Moyes' side will know they can compete against whoever they face in the one-off format of a cup.
As well as being consistent at grinding out results, as a rule, Everton have become especially hard to beat over the past 12 months.
Moyes' side have only lost three games all season, a tally only Manchester City can beat. They are currently on a run of just three defeats in 32 and five in their last 41 matches, illustrating their resilience.
Draws may have been hampering their league form, but few sides have been able to see off this current squad of players, which augurs well for this cup run.
Regardless of their opponent, Everton will be confident they can remain in the contest right until the end.
A reason for some of the Toffees' recent FA Cup success is the amount of fervent support travelling with them.
Goodison Park can be a hostile venue for most visiting sides, but it's on the road where Evertonians can be most effective.
Bumper attendances have accompanied the Toffees across the land and the recent atmospheres created at Sunderland and Chelsea in the past few seasons have been hugely influential.
The away allocation for Saturday's trip to Bolton is typically sold out, and Everton will hope their supporters can once again make a difference.
Finally, another reason to believe in Everton's current cup credentials is due to the man plotting their progress.
David Moyes is one of the most respected managers in England, yet for all he's achieved in more than a decade at Everton, he's never been able to claim silverware.
This is something he's desperate to rectify.
With his contractual situation up in the air, this is his best opportunity to land a trophy and mark his tenure with the Toffees
With Moyes leading their charge, Everton won't go down without a fight in this season's competition.