The Glovers were knocked out by Manchester United in the next round but it started a long association between the club and the competition.
Town defeated 20 Football League teams in the tournament until eventually becoming one themselves in 2003.
Saturday represents a chance to overcome higher league opposition in Southend United at Huish Park.
Fresh from scoring a home brace last weekend, AFC Bournemouth loanee Sam Surridge is likely to lead the line with Olufela Olomola and Francois Zoko serving the first of their three-game bans.
Jordan Green could come into contention after recovering from an injury and Ryan Dickson (concussion) returned to training on Monday.
Southend haven’t reached the second round of the FA Cup since 2013.
The Shrimpers sit 11th in League One and have aims of making the play-offs after missing out by one point in 2016/17.
They have a lot of experience with Anton Ferdinand, Simon Cox, Michael Turner, Michael Kightly and Marc-Antoine fortune all in their squad.
It is the fourth meeting between the two sides in the FA Cup (plus a replay) but the first since Yeovil entered the EFL.
In the competition, Town have won twice and drawn once, losing the 1982 replay.
Since 2003, the Glovers have faced the Shrimpers 13 times winning seven times (D2 L4).
Craig Hicks (Surrey) will take charge on Saturday.
The match will be the official’s 16th game this season. He issued 63 yellow cards and three reds.
Hicks took charge of Yeovil’s 2-2 draw with Morecambe earlier on in the Sky Bet League Two term.
He will be assisted by Simon Shaw (Gloucestershire) and Mark Derrien (Dorset) with Dean Treleaven (West Sussex) acting as fourth official.
Darren Way and Otis Khan’s pre-match thoughts can be watched in full for free on iFollow Glovers.
If you’re unable to attend the game, live audio commentary is available via the iFollow Glovers service, with the monthly and season subscriptions offering full-match replays from Sunday.
A full match report will follow on YTFC.net at full-time with post-match reaction from the manager and a member of the playing staff following soon after.