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Latics booked their place with a 2-1 extra-time win over League One Sheffield Wednesday, with goals from Calum Kavanagh and Will Sutton.
They must now overcome League Two rivals if they are to earn a place in the coveted third round after being handed a trip to Blundell Park.
The draw was made live on TNT Sports, who broadcast the game live from Boundary Park last night.
The full draw for the second round is as follows:
Chesterfield v Cheltenham Town
Guiseley v Notts County
Wigan Athletic v Barnsley
Exeter City v Stevenage
Plymouth Parkway/Berkhamsted v Barnet
York City v Carlisle
Crewe Alexandra v Plymouth Argyle
AFC Fylde v Luton Town
Barrow v Kidderminster Harriers
Colchester v Mansfield Town
Rochdale v Newport County
Dover Athletic v Leicester City
Port Vale v Leyton Orient
Grimsby Town v Oldham Athletic
Shrewsbury Town v Burton Albion
Salisbury v Blackpool
Wimborne Town v Bradford City
Rotherham v Bristol Rovers
Reading v Stockport County
Wycombe Wanderers v MK Dons