Prize money of £9,375 – alongside a place in Sunday's televised first round draw – is up-for-grabs for the winners at Sandy Lane.
The sides have not met competitively since 2010, when the Pilgrims earned promotion via the UniBond Premier League play-offs.
The Tigers are now back at Step 3 and are expecting to challenge for promotion themselves this season – with a strong home record to boot.
Craig Parry's side, who could include ex-Pilgrims Paul Green, Terry Hawkridge, Jack Broadhead, Jay Rollins and James Hanson, have defeated Sheffield FC, Lincoln United and Blyth Spartans (after a replay) in the FA Cup so far this season.
Should a replay be required, it will be staged at the Jakemans Community Stadium on Tuesday evening (kick-off 7.45pm).
LIVE COVERAGE
BBC Radio Lincolnshire full-match commentary, courtesy of Dale Storey and Craig Singleton, is available.
Twitter updates will be available via @bostonunited throughout the afternoon.
TICKETS
Online tickets have now gone off sale. Away supporters can pay by cash or card on the turnstiles.
KIT WATCH
United will be wearing their third kit of all-white.
PIC: Chris Bray.