Michael Boulding's 80th minute goal took the Mariners through against QPR at Blundell Park on Saturday.
Town boss Paul Groves had admitted that he wanted another home-tie but will still view this game as one his team can win.
The Posh went through to the second round with a 2-0 win over Conference outfit Hereford at London Road.
Loan strikers Calum Willock and Richard Logan getting the goals for Barry Fry's men.
The game will take place the weekend of 6 December
Full Draw:
Northampton v Weston Super Mare
Rochdale v Thurrock/Luton
Colchester v Aldershot
Macclesfield v Cambridge
Peterborough v Grimsby
Bristol City v Barnsley
Oldham v Blackpool
Burton Albion v Hartlepool
Gravesend v Notts County
Telford v Brentford
Woking v Kidderminster
Hornchurch v Tranmere
Bournemouth v Accrington
Cheltenham v Leyton Orient
Yeovil v Barnet/Stalybridge
Port Vale/Ford Utd v Scarborough
Wycombe v Mansfield
Southend/Canvey Island v Lincoln City
Scunthorpe v Sheff Wed
Swansea v Stevenage
