FA Cup giant killers Salford City will face Hartlepool United in the second round.
The Northern Premier Division side, owned by five of Manchester United’s class of ’92, advanced after beating League One Notts County 2-0 on Friday night.
Hartlepool, in League Two and managed by the experienced Roonie Moore, make the trip to Moor Lane after defeating Cheltenham Town 1-0.
The lowest ranked team left in the competition are Northwich Victoria, and if they see off Boreham Wood in a replay, they will visit League Two promotion chasers Northampton.
Southern League Premier Division side Chesham United pulled off a shock 1-0 win at Bristol Rovers on Sunday, and their reward is an away tie against either National League Aldershot or League One Bradford, who need a replay after a goalless draw,
Following their surprise win over Dover, seventh-tier outfit Stourbridge are also eyeing the third round after they were picked out to play National League side Eastleigh at home.
After reaching the second round for the first time in their history, Sussex side Whitehawk have been handed an away tie to either Dagenham & Redbridge or Morecambe, both of League Two.
Brackley Town could also play a fourth-tier side away from home if they see off Newport County in a reply, with Barnet awaiting in round two, while Maidenhead will travel to Exeter City if they win their replay with Port Vale.
Elsewhere, Walsall – currently the highest-ranked team in the second round – play Chesterfield, who defeated FC United of Manchester, while Welling United welcome Carlisle United to South London and 2008 winners Portsmouth play Accrington Stanley at Fratton Park.
Second Round Draw:
Aldershot/Bradford City v Chesham United
Barnet v Brackley Town/Newport County
Peterborough v Luton
Portsmouth v Accrington Stanley
Stourbridge v Eastleigh
Northampton Town v Northwich/Boreham Wood
Exeter v Port Vale/Maidenhead United
Cambridge United v Doncaster Rovers
Grimsby v Shrewsbury
Yeovil Town v Stevenage
Rochdale v Bury
Welling United v Carlisle
Leyton Orient v Scunthorpe
Millwall v Wycombe
Colchester United v Altrincham
Chesterfield v Walsall
Sheffield United v Mansfield/Oldham
Salford City v Hartlepool
Dagenham & Redbridge/Morecambe v Whitehawk
Braintree/Oxford v Forest Green
All ties to be played across the weekend of 4-7 December 2015.