Luton, now in the fifth tier of English football, are rewarded for beating Championship Wolves with a visit to Norwich in the fourth round.
Macclesfield, who overcame Cardiff City on Saturday, will host the winners of a replay between Bournemouth and Wigan.
The Premier League's top clubs avoided one another, although there is the prospect of a repeat of the 2011 FA Cup final should Stoke City defeat Crystal Palace in a replay and set up a showdown with Manchester City.
The games will be played over the weekend of January 26/27.
Full fourth round draw:
Norwich City v Luton Town
Oldham Athletic v Liverpool
Macclesfield Town v Wigan Athletic/Bournemouth
Derby County v Blackburn Rovers
Hull City/Leyton Orient v Barnsley
Middlesbrough v Aldershot
Millwall v Aston Villa
Leeds United/Birmingham City v Tottenham Hotspur
Brighton & Hove Albion v Swansea City/Arsenal
Crystal Palace/Stoke City v Manchester City
West Ham United/Manchester United v Fulham/Blackpool
Southend United/Brentford v Chelsea
Reading v Sheffield United
Huddersfield Town v Leicester City
QPR/West Brom v Sheffield Wednesday/MK Dons
Bolton Wanderers/Sunderland v Cheltenham/Everton
