National League South side Slough Town - the lowest-ranked team left in the competition, 21st in the sixth tier - will host National League North Macclesfield, while South side Chelmsford City will be at home to Weston-super-Mare.
The winners of the final first round proper tie, National League Tamworth versus League OneLeyton Orient, will be away at Salford City in the last round before the Premier League and Championship teams enter the fray.
Carlisle - who - have been rewarded with a trip to League One side Blackpool, while fellow giant-killers Gateshead, who downed League One's AFC Wimbledon 2-0, will host fourth-tier leaders Walsall.
In total 11 non-league sides, including five sixth-tier teams, progressed to the second round, with Tamworth potentially set to join them after the conclusion of Monday's fixture.
Boreham Wood, who dumped League Two's Crawley out, will be at home to another League Two side, Newport County, who sit just three places above them in prime 'cupset' territory.
League One's Wigan Athletic, who made a narrow escape on penalties against National League South team Hemel Hempstead, are at home to fourth-tier Barrow. Brackley Town, who edged past Notts County on penalties, will host Burton Albion.
The draw took place at The Lamb Ground, home of minnows Tamworth, before their game against Leyton Orient. The second round ties will be played from 5-8 December.
Here is the full list of fixtures:
Slough Town vs Macclesfield FC
Grimsby Town vs Wealdstone
Sutton United vs Shrewsbury Town
Swindon Town vs Bolton Wanderers
Chelmsford City vs Weston-super-Mare
Peterborough United vs Barnsley
Boreham Wood vs Newport County
MK Dons vs Oldham Athletic
Wigan Athletic vs Barrow
Fleetwood Town vs Luton Town
Salford City vs Tamworth or Leyton Orient
Accrington Stanley vs Mansfield Town
Stockport County vs Cambridge United
Brackley Town vs Burton Albion
Blackpool vs Carlisle United
Gateshead vs Walsall
Exeter City vs Wycombe Wanderers
Cheltenham Town vs Buxton
Chesterfield vs Doncaster Rovers
Port Vale vs Bristol Rovers