The draw for round two - the final stage before all the Premier League and Championship sides enter - was screened live on BBC Two. Giant killers of Round 1, Salford City have been drawn at home to League Two Hartlepool United
The Northern Premier League Premier Division side, co-owned by five former Manchester United players, defeated Notts County in the first round.
Northwich Victoria, the lowest ranked side, visit League Two Northampton if they defeat Boreham Wood in a replay.
Seventh-tier Stourbridge will join Premier League clubs in the third round if they defeat Eastleigh.
Southern League Premier Division Chesham United's reward for winning at Bristol Rovers is a trip to the winners of the replay between National League Aldershot and League One Bradford.
Second-round ties will be played across the weekend of 4-7 December 2015.
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
FC United/Chesterfield v Walsall
Sheffield United v Mansfield/Oldham
Salford City v Hartlepool
Dagenham & Redbridge/Morecambe v Whitehawk
Braintree/Oxford v Forest Green