To reach this stage, the Toffees disposed of League Two Cheltenham in the previous round, by a convincing 5-1 scoreline.
Championship Bolton were less emphatic, but secured an equally impressive 2-0 win away at Premier League Sunderland, having originally been held to a 2-2 draw.
Here's a look at some team news and a possible Everton selection for Saturday's clash.
No longer divisional rivals following the Trotters' 2012 relegation, these two sides have still faced each other twice each season over the past 11 Premier League campaigns.
In those 22 most recent ties, Everton have been victorious 11 times, Bolton seven and there have been four draws.
The last time this pair met in the FA Cup was way back in 1994. A certain Alan Stubbs—now the Toffees' reserve team coach—grabbed a crucial goal for Bolton, as the Trotters triumphed in a shock 3-2 win.
The last four ties played on Bolton's turf have been split, with two wins each, and their last meeting is especially remembered for Tim Howard's goal from his own area.
Kevin Mirallas appeared as a substitute in Monday's game at Southampton, continuing his latest recovery from injury.
He may well continue his rehabilitation at Bolton, perhaps featuring for a longer period.
Tony Hibbert remains a long-term absentee, with Seamus Coleman joining him after he was withdrawn through injury against Southampton.
However, Darron Gibson is now said to be nearing a return (via EvertonFC.com)
In Mark Davies, David Wheater and Stuart Holden, Bolton have had a trio of influential players missing for a considerable length of time.
All of them are now nearing a full return and could figure at some point this weekend (per EvertonFC.com).
Craig Dawson is cup-tied while Keith Andrews and Matt Mills look set to miss out with injury (via the Guardian).
Tim Howard; Phil Neville, Phil Jagielka, John Heitinga, Bryan Oviedo; Steven Naismith, Marouane Fellaini, Leon Osman, Steven Pienaar; Kevin Mirallas; Victor Anichebe.
Judging by his lineup in the previous round at Cheltenham, it seems David Moyes is intent on playing his strongest side throughout the FA Cup. Therefore, expect Tim Howard to start in goal.
In front of him, Leighton Baines has been playing with an ankle injury and may get a rest, allowing Oviedo to come in. The Costa Rican has recently impressed in Everton's second-string and is due a run-out.
Elsewhere, in defence, Heitinga may be given a game to allow Sylvain Distin an afternoon off, but otherwise Moyes is likely to go for his strongest selection.
Further up the pitch, Moyes could well deploy his midfield as they finished on Monday. That would mean Fellaini dropping deeper with Osman in the middle, flanked by Pienaar and Naismith.
In attack, Anichebe was one of the few to impress against Southampton. The Nigerian should start, and it would make sense to bring in Mirallas just off him, to step up his return to fitness.
After a patchy few months, Nikica Jelavic may be used from the bench in this one.
Alternatively, Moyes could opt for Mirallas as a substitute, or in place of Naismith, and keep Jelavic in attack, supported by Anichebe.