And Northwich Victoria, the lowest ranked side left in the competition, will travel to League Two Northampton Town if they can get past National League Boreham Wood in their replay following Monday night's televised draw on BBC2.
Hosted by Mark Chapman, the draw at the Civil Service FC's King's Head ground in west London handed all three of the EVO-STIK NPL's flag-bearers a real chance of reaching the FA Cup's Third Round and banking another £27,000 in prize money on route, not to mention any TV fees that could come their way after their heroics at the weekend.
The Ammies, 2-0 winners over Notts County on Friday night in front of millions watching on the BBC, will fancy their chances again when they welcome Hartlepool United to Moor Lane after Blyth Spartans knocked the League Two side out at the same stage last year.
The Glassboys, 2-1 winners at National League Dover Athletic at the weekend, were also rewarded with a home tie against the Spitfires but will be wary with their opponents currently flying high in the National League.
Jim Gannon's First Division North leaders must first beat the Wood in Hertfordshire after drawing 1-1 at Wincham Park before heading to the Sixfields Stadium to take on the Cobblers in the ties which are all scheduled to take place over the weekend of Saturday 5 December.
FA Cup Second Round Draw
Aldershot or Bradford City v Chesham United
Barnet v Brackley Town or Newport County
Peterborough v Luton
Portsmouth v Accrington Stanley
Stourbridge v Eastleigh
Northampton Town v Northwich Victoria or Boreham Wood
Exeter v Port Vale or 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 of Manchester or Chesterfield v Walsall
Sheffield United v Mansfield or Oldham
Salford City v Hartlepool
Dagenham & Redbridge or Morecambe v Whitehawk
Braintree or Oxford v Forest Green
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