Salford City have been drawn at home to League Two Hartlepool United in the second round of the FA Cup.
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.
"We'll have to make sure the players are mentally right and prepared for it," said Chris Todd, manager of fifth-tier Eastleigh.
That tie will guarantee that there will be at least one non-league side in the third round of the competition.
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.
Chesterfield will host League One leaders Walsall, the highest ranked side at this stage, after defeating FC United of Manchester 4-1 in the first round on Monday night.
"It is going to be tough but we have a home draw and that is all we could have asked for," said Chesterfield boss Dean Saunders after his team's win.
Sixth-tier Brackley Town face a trip to Barnet if the non-League side see off Newport County in a replay - and boss Kevin Wilkin said: "It's a tough draw but we have another game to think about first.
"Our aim is to get through, stay in the hat, it's another opportunity for us."
National League South Whitehawk face a trip to League Two Morecambe or Dagenham & Redbridge, while Maidenhead United are away to League Two Exeter if the non-League side defeat Port Vale in a replay.
The draw for round two - the final stage before all the Premier League and Championship sides enter - was screened live on BBC Two.
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
Chesterfield v Walsall
Sheffield United v Mansfield/Oldham
Salford City v Hartlepool
Dagenham & Redbridge/Morecambe v Whitehawk
Braintree/Oxford v Forest Green