Liverpool will host Merseyside neighbours Everton in the FA Cup third round – one of a handful of local derbies thrown up in Monday's draw.
Jurgen Klopp's men host Everton in their first Premier League clash of the season on Sunday and will now meet again over the weekend of January 5-8.
It will be the first FA Cup derby between the sides since Liverpool prevailed 2-1 in a 2012 semi-final – the Reds going on to lose to Chelsea in the final by the same margin.
Brighton & Hove Albion are at home to Crystal Palace having played out a goalless Premier League draw against their bitter rivals last week, while Middlesbrough welcome Sunderland in an all north-east affair.
Holders Arsenal will begin their bid for a 14th FA Cup away to Nottingham Forest, with last season's beaten finalists Chelsea also travelling to face Championship opposition in the form of Norwich City.
Wimbledon famously upset Liverpool at Wembley in the 1988 final and League One AFC Wimbledon will try their luck at the national stadium against Tottenham.
Premier League leaders Manchester City are at home to Burnley – the third and final all top-flight tie – and Manchester United are at home to Derby County.
Swansea City, bottom of the Premier League, face Championship leaders Wolves at Molineux.
Seventh-tier Slough Town are the lowest ranked team left in the competition and will try to upset League One Rochdale and claim a round-three trip to Doncaster Rovers.
Fellow non-league teams Hereford, AFC Fylde and Woking will play Leicester City, Bournemouth and Aston Villa if they are able to overcome respective replays with Fleetwood Town, Wigan Athletic and Peterborough United.
FA Cup third round – draw in full:
Ipswich Town v Sheffield United
Watford v Bristol City
Birmingham City v Burton Albion
Liverpool v Everton
Brighton & Hove Albion v Crystal Palace
Aston Villa v Woking or Peterborough United
Bournemouth v AFC Fylde or Wigan Athletic
Coventry City v Stoke City
Newport County v Leeds United
Bolton Wanderers v Huddersfield Town
Port Vale or Yeovil Town v Bradford City
Nottingham Forest v Arsenal
Brentford v Notts County
Queens Park Rangers v MK Dons
Manchester United v Derby County
Forest Green Rovers or Exeter City v West Brom
Doncaster Rovers v Slough Town or Rochdale
Tottenham v AFC Wimbledon
Middlesbrough v Sunderland
Fleetwood Town or Hereford v Leicester City
Blackburn Rovers or Crewe Alexandra v Hull City
Cardiff City v Mansfield Town
Manchester City v Burnley
Shrewsbury Town v West Ham
Wolves v Swansea City
Stevenage v Reading
Newcastle United v Luton Town
Millwall v Barnsley
Fulham v Southampton
Wycombe Wanderers v Preston North End
Norwich City v Chelsea
Gillingham or Carlisle v Sheffield Wednesday