The FA Cup holders Chelsea will begin their defence against Nottingham Forest at Stamford Bridge when the third round begins in January.
Wolves vs Liverpool and Bournemouth vs Brighton were the only all-Premier League ties drawn, while National League North side Solihull Moors drew a dream home tie against Arsenal, although they will have to get past a second-round replay with Blackpool to meet Unai Emery’s Gunners.
Tottenham, who lost Sunday's north London derby at Arsenal, will travel to either League Two Tranmere or National League North Southport.
Cardiff will travel to League One Gillingham, while Newcastle face Championship Blackburn at St James’ Park and Crystal Palace are at home to League Two Grimsby.
Managerless Southampton have been drawn away to Frank Lampard’s promotion-chasing Derby, while Fulham welcome League Two Oldham to Craven Cottage and Championship side Birmingham head for West Ham, with Burnley taking on League One Barnsley at Turf Moor.
Ties will be played on 4-7 January.
Full FA Cup third-round draw:
Bolton v Walsall/Sunderland
Millwall v Hull
Gillingham v Cardiff
Brentford v Oxford
Sheffield Wed v Luton
Man Utd v Reading
Everton v Lincoln
Tranmere/Southport v Tottenham
Preston v Doncaster
Newcastle v Blackburn
Chelsea v Nottingham Forest
C Palace v Grimsby
Derby v Southampton
Accrington v Ipswich
Bristol City v Huddersfield
Wrexham/Newport v Leicester
Fulham v Oldham
Shrewsbury v Stoke
Solihull Moors/Blackpool v Arsenal
Man City v Rotherham
Bournemouth v Brighton
West Ham v Birmingham
Woking v Watford
Burnley v Barnsley
QPR v Leeds
Sheffield Utd v Barnet
Norwich v Portsmouth
Guiseley/Fleetwood v AFC Wimbledon
West Brom v Wigan
Middlesbrough v Peterborough/Bradford
Wolves v Liverpool
Aston Villa v Swansea
