The damage was done thanks to goals from Paul Hayes and Ian Baraclough, either side of the interval.
Progression earned United £16,000 and saw them into this evening's second round draw, which was made live on BBC1.
The tie will be played on December 4, unless it is moved on police advice or to accomodate the TV cameras.
Draw in full:
Northampton v Bury, Halifax Town v Chester City, Stockport County v Swansea City, Blackpool v Port Vale, Rushden & Diamonds v Mansfield Town or Colchester, Forest Green or Bournemouth v Bristol Rovers or Carlisle, Hinckley United v Bristol City or Brentford, Cambridge City v Milton Keynes Dons, Swindon Town v Notts County, Hull City v Alfreton or Macclesfield, Wycombe Wanderers v Luton Town, Slough Town v Yeading, Scunthorpe United v Wrexham, Histon v Darlington or Yeovil Town, Stevenage Borough v Rochdale, Hartlepool United v Aldershot Town, Oldham Athletic v Leyton Orient, Hereford United v Boston United, Peterborough United v Bath City, Exeter City v Doncaster Rovers
