Alex Ferguson's side lost 1-0 at home to a Paolo Di Canio-inspired West Ham in the 2001 FA Cup, but thumped the Hammers 6-0 two years later.
Holders Chelsea also face an away match against Premier League opponents in the shape of Southampton, while Arsenal visit Swansea.
QPR, still winless in the Premier League, take on West Bromwich Albion, while Manchester City are at home to Championship side Watford.
Tottenham Hotspur face Coventry City 25 years after the Sky Blues' victory in the 1987 final.
A plum tie awaits the winner of the replay between non-leaguers Lincoln City and Mansfield Town - they will play Liverpool at home.
FA CUP THIRD ROUND DRAW
Crystal Palace v Stoke City
Brighton and Hove Albion v Newcastle United
Tottenham Hotspur v Coventry City
Wigan Athletic v AFC Bournemouth
Fulham v Blackpool
Aston Villa v Ipswich
Charlton Athletic v Huddersfield Town
Barrow or Macclesfield v Cardiff City
Barnsley v Burnley
Manchester City v Watford
Swansea City v Arsenal
Leicester City v Burton Albion
Millwall v Preston North End
Cheltenham or Hereford v Everton
Derby County v Tranmere Rovers
Crawley Town v Reading
Aldershot Town v Rotherham or Notts County
Middlesbrough v Harrogate or Hastings
Accrington or Oxford v Sheffield United
Southampton v Chelsea
QPR v West Bromwich Albion
Peterborough United v Norwich City
Lincoln or Mansfield v Liverpool
Bolton Wanderers v Sunderland
Nottingham Forest v Oldham Athletic
West Ham v Manchester United
Hull City v Alfreton or Leyton Orient
Blackburn Rovers v Bristol City
Leeds United v Birmingham City
Bury or Southend v Bradford or Brentford
Luton Town v Wolverhampton Wanderers
Sheffield Wednesday v Milton Keynes Dons
Matches to be played weekend January 5-6
