The Welsh club were in the old Division Four when they ousted Arsenal in the third round in 1992, with the aid of a stunning free-kick from former Stoke midfielder Mickey Thomas.
Now in the Conference, Wrexham head to the Britannia Stadium looking to spring another surprise against a top-flight side.
Stoke manager Mark Hughes was born in Wrexham and is unlikely to need any reminding of his hometown club's capacity to upset the odds in the FA Cup.
While Stoke - FA Cup finalists in 2011 - will be strong favourites to progress to round four on this occasion, the visitors' hopes could be enhanced by Hughes' team selection, with the 51-year-old expected to make a host of changes following a busy festive schedule.
The likes of Jack Butland, Robert Huth and Charlie Adam are among those likely to come into contention should Hughes, who will be without the injured Bojan Krkic (hamstring), opt to rest a number of his first-team regulars.
Stoke could also hand a maiden start to highly rated 17-year-old midfielder Oliver Shenton, an unused substitute in the club's last two Premier League matches who made his senior debut in the League Cup earlier this season.
Wrexham are sweating on the fitness of top scorer Louis Moult, a 22-year-old striker who made a solitary league appearance for Stoke against Burnley in 2009 after coming through the club's academy set-up.
Moult picked up an ankle injury during a Boxing Day victory over Southport, which saw Kevin Wilkin's men rise to 14th in the Conference table.
Goalkeeper Daniel Bachmann has been on loan at Wrexham from Stoke this season, but that deal has now expired, meaning Jon Flatt - another loanee - is likely to start in between the posts on Sunday.
"The pressure for this game is all on Stoke, we have to use this to our advantage," Flatt, who is on loan from Wolves, told Wrexham's official website.
"Going to Stoke for anybody, even a Premier League team, is a tough ask. Obviously we are all going to have to stick together, but we are determined to come out of the game having given a good account of ourselves.
"We need to stick together as a team and most importantly enjoy the occasion; not many Conference players get to play against a Premier League team in the FA Cup."
Wrexham, who have not reached the fourth round since the 1999-2000 season, are set to be roared on by a healthy following, having requested extra tickets from Stoke after selling out their initial allocation of 4,300.
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