Defending Johnstone's Paint Trophy champions Doncaster will play League one rivals Oldham in the second round.
Leeds, who were deducted 15 points at the start of the season, face a visit to Darlington in the northern section.
In the southern section, League One pacesetters Leyton Orient will play Dagenham & Redbridge.
In a change to last season, both the northern and southern sections will be sub-divided for round two and the ties will be in the week starting 8 October.
There is one outstanding first-round tie between Wrexham and Macclesfield, in the north-west section, which will be played on Tuesday 18 September.
The game was postponed because of Wrexham's international call-ups.
Northern Section
Wrexham/Macclesfield v Stockport
Carlisle v Chester
Morecambe v Port Vale
Rochdale v Bury
Doncaster v Oldham
Darlington v Leeds
Lincoln City v Hartlepool
Rotherham v Grimsby
Southern Section
Hereford v Yeovil
Bristol Rovers v Bournemouth
Swindon v Cheltenham
Swansea v Wycombe
Milton Keynes Dons v Peterborough
Brighton v Barnet
Leyton Orient v Dagenham & Redbridge
Gillingham v Luton
Remaining dates for this season's Johnstone's Paint Trophy:
Second round: Week commencing 8 October
Area quarter-finals: Week commencing 12 November
Area semi-finals: Week commencing 7 January
Area finals (first leg): Week commencing 18 February
Area finals (second leg): Week commencing 25 February
Final: Sunday, 30 March
Bookmark with:
What are these?