Northwich Victoria emulated Kettering's result on Sunday with a deserved 1-0 home win over League One promotion-hopefuls Charlton and they now host Chris Sutton's Lincoln after Sunday's draw was made at Wembley.
Staines Town of the Blue Square South, the conquerors of Shrewsbury in the first round, could meet another League One team in Millwall, if the Lions see off AFC Wimbledon on Monday.
York, who ended Crewe's hopes in the last round, were given a tricky-looking trip to Blue Square Premier rivals Cambridge United.
Blue Square South side Bath City, who beat Grimsby, were paired with Forest Green or Mansfield.
FA Cup second-round draw in full: Northwich v Lincoln City, Northampton v Southampton, Hereford v Colchester, Tranmere/Leyton Orient v Aldershot, Kettering v Leeds, Gillingham v Burton Albion/Oxford City, Wrexham v Swindon, Wycombe/Brighton v Rushden & Diamonds, Wealdstone/Rotherham v Luton/Rochdale, MK Dons v Exeter, Gateshead/Brentford v Walsall, Carlisle/Morecambe v Norwich, Accrington v Barnet, Oxford Utd v Barrow, Bournemouth v Notts County, Stockport v Torquay, Cambridge Utd v York, Bath v Forest Green/Mansfield, Port Vale/Stevenage v Huddersfield, Staines v Millwall/AFC Wimbledon.
Ties to be played over the weekend of November 28 and 29.